Almost periodic-type functions and their applications: Survey of recent results and further perspectives

References

[1] F. G. Abdullayev, P. Özkartepe, V. V. Savchuk and A. L. Shidlich, Exact constants in direct and inverse approximation theorems for functions of several variables in the spaces 𝒮 p , Filomat 33 (2019), no. 5, 1471–1484. 10.2298/FIL1905471ASuche in Google Scholar

[2] G. Akagi and U. Stefanelli, Periodic solutions for doubly nonlinear evolution equations, J. Differential Equations 251 (2011), no. 7, 1790–1812. 10.1016/j.jde.2011.04.014Suche in Google Scholar

[3] M. Akhmet, M. Tleubergenova and A. Zhamanshin, Modulo periodic Poisson stable solutions of quasilinear differential equations, Entropy 23 (2021), no. 11, Paper No. 1535. 10.3390/e23111535Suche in Google Scholar PubMed PubMed Central

[4] N. T. V. Anh, On periodic solutions to a class of delay differential variational inequalities, Evol. Equ. Control Theory 11 (2022), no. 4, 1309–1329. 10.3934/eect.2021045Suche in Google Scholar

[5] N. T. V. Anh and T. D. Ke, Asymptotic behavior of solutions to a class of differential variational inequalities, Ann. Polon. Math. 114 (2015), no. 2, 147–164. 10.4064/ap114-2-5Suche in Google Scholar

[6] D. G. Aronson and H. F. Weinberger, Multidimensional nonlinear diffusion arising in population genetics, Adv. Math. 30 (1978), no. 1, 33–76. 10.1016/0001-8708(78)90130-5Suche in Google Scholar

[7] C. Arzelà, Sulle funzioni di più variabili a variazione limitata, Rend. Accad. Sci. Bologna 9 (1905), no. 2, 100–107. Suche in Google Scholar

[8] E. R. Attia and B. M. El-Matary, New aspects for the oscillation of first-order difference equations with deviating arguments, Opuscula Math. 42 (2022), no. 3, 393–413. 10.7494/OpMath.2022.42.3.393Suche in Google Scholar

[9] E. P. Avgerinos and N. S. Papageorgiou, Differential variational inequalities in 𝐑 N , Indian J. Pure Appl. Math. 28 (1997), no. 9, 1267–1287. Suche in Google Scholar

[10] M. Ayachi, Measure-pseudo almost periodic dynamical behaviors for BAM neural networks with D operator and hybrid time–varying delays, Neurocomputing 486 (2022), 160–173. 10.1016/j.neucom.2021.11.020Suche in Google Scholar

[11] A. Bahri and H. Brézis, Periodic solution of a nonlinear wave equation, Proc. Roy. Soc. Edinburgh Sect. A 85 (1980), no. 3–4, 313–320. 10.1017/S0308210500011896Suche in Google Scholar

[12] E. G. Bajlekova, Fractional evolution equations in Banach spaces, Ph.D. Thesis, Eindhoven University of Technology, Eindhoven, 2001. Suche in Google Scholar

[13] N. R. Bantsur and O. P. Trofimchuk, Existence and stability of periodic and almost periodic solutions of quasilinear equations with maxima, Ukrainian Math. J. 50 (1998), 847–856. 10.1007/BF02515218Suche in Google Scholar

[14] N. R. Bantsur and O. P. Trofimchuk, On the existence of T-periodic solutions of essentially nonlinear scalar differential equations with maxima, Nelīnīĭnī Koliv. (1998), no. 1, 1–5. Suche in Google Scholar

[15] V. Barbu and N. H. Pavel, Periodic solutions to nonlinear one-dimensional wave equation with x-dependent coefficients, Trans. Amer. Math. Soc. 349 (1997), no. 5, 2035–2048. 10.1090/S0002-9947-97-01714-5Suche in Google Scholar

[16] F. Bayart and E. Matheron, Dynamics of Linear Operators, Cambridge Tracts in Math. 179, Cambridge University, Cambridge, 2009. 10.1017/CBO9780511581113Suche in Google Scholar

[17] O. Benchiheb, S. Ivković and M. Kostić, Almost periodic dynamics of binary relations, preprint. Suche in Google Scholar

[18] H. Berestycki and F. Hamel, Front propagation in periodic excitable media, Comm. Pure Appl. Math. 55 (2002), no. 8, 949–1032. 10.1002/cpa.3022Suche in Google Scholar

[19] H. Berestycki, F. Hamel and G. Nadin, Asymptotic spreading in heterogeneous diffusive excitable media, J. Funct. Anal. 255 (2008), no. 9, 2146–2189. 10.1016/j.jfa.2008.06.030Suche in Google Scholar

[20] H. Berestycki, F. Hamel and L. Roques, Analysis of the periodically fragmented environment model. I. Species persistence, J. Math. Biol. 51 (2005), no. 1, 75–113. 10.1007/s00285-004-0313-3Suche in Google Scholar PubMed

[21] H. Berestycki, F. Hamel and L. Roques, Analysis of the periodically fragmented environment model. II. Biological invasions and pulsating travelling fronts, J. Math. Pures Appl. (9) 84 (2005), no. 8, 1101–1146. 10.1016/j.matpur.2004.10.006Suche in Google Scholar

[22] H. Berestycki, F. Hamel and L. Rossi, Liouville-type results for semilinear elliptic equations in unbounded domains, Ann. Mat. Pura Appl. (4) 186 (2007), no. 3, 469–507. Suche in Google Scholar

[23] H. Berestycki, F. Hamel and L. Rossi, Liouville-type results for semilinear elliptic equations in unbounded domains, Ann. Mat. Pura Appl. (4) 186 (2007), no. 3, 469–507. 10.1007/s10231-006-0015-0Suche in Google Scholar

[24] H. Berestycki and L. Nirenberg, Travelling fronts in cylinders, Ann. Inst. H. Poincaré C Anal. Non Linéaire 9 (1992), no. 5, 497–572. 10.1016/s0294-1449(16)30229-3Suche in Google Scholar

[25] H. Berestycki, L. Nirenberg and S. R. S. Varadhan, The principal eigenvalue and maximum principle for second-order elliptic operators in general domains, Comm. Pure Appl. Math. 47 (1994), no. 1, 47–92. 10.1002/cpa.3160470105Suche in Google Scholar

[26] L. Berezansky and E. Braverman, On existence of positive solutions for linear difference equations with several delays, Adv. Dyn. Syst. Appl. 1 (2006), no. 1, 29–47. 10.1155/ADE/2006/82143Suche in Google Scholar

[27] A. Berger, S. Siegmund and Y. Yi, On almost automorphic dynamics in symbolic lattices, Ergodic Theory Dynam. Systems 24 (2004), no. 3,´677–696. 10.1017/S0143385703000609Suche in Google Scholar

[28] J. Bergh and J. Löfström, Interpolation Spaces, Springer, Berlin, 1976. 10.1007/978-3-642-66451-9Suche in Google Scholar

[29] S. N. Bernšteĭn, On the best approximation of continuous functions by polynomials of given degree (in Russian), Collected Works. 1, Acad. Nauk SSSR, Moscow (1952), 11–104. Suche in Google Scholar

[30] A. S. Besicovitch, Almost Periodic Functions, Dover, New York, 1954. Suche in Google Scholar

[31] G. D. Birkhoff, Dynamical Systems, Amer. Math. Soc. Colloq. Publ. 9, American Mathematical Society, Providence, 1966. Suche in Google Scholar

[32] I. N. Blinov, Regularity of a class of linear systems with almost periodic coefficients (in Russian), Differ. Uravn. 3 (1967), 764–768. Suche in Google Scholar

[33] I. N. Blinov, The reduction of a class of systems with almost periodic coefficients (in Russian), Mat. Zametki 2 (1967), 395–400. 10.1007/BF01093650Suche in Google Scholar

[34] I. N. Blinov, An application of a method of arbitrarily rapid convergence to the solution of the problem of reducibility of linear systems with odd almost periodic coefficients (in Russian), Mat. Zametki 4 (1968), 729–740. 10.1007/BF01110831Suche in Google Scholar

[35] I. N. Blinov, A certain qualitative characterization of the class of reducible systems with quasi-periodic coefficients (in Russian), Differ. Uravn. 11 (1975), no. 6, 955–960, 1147. Suche in Google Scholar

[36] I. N. Blinov, Absence of exact mean values for certain bounded functions (in Russian), Izv. Akad. Nauk SSSR Ser. Mat. 47 (1983), no. 6, 1162–1181. Suche in Google Scholar

[37] L. S. Block and W. A. Coppel, Dynamics in One Dimension, Lecture Notes in Math. 1513, Springer, Berlin, 1992. 10.1007/BFb0084762Suche in Google Scholar

[38] J. Blot, Oscillations presque-périodiques forcées d’équations d’Euler–Lagrange, Bull. Soc. Math. France 122 (1994), no. 2, 285–304. 10.24033/bsmf.2233Suche in Google Scholar

[39] F. Brandt and M. Hieber, Strong periodic solutions to quasilinear parabolic equations: An approach by the Da Prato–Grisvard theorem, Bull. Lond. Math. Soc. 55 (2023), no. 4, 1971–1993. 10.1112/blms.12831Suche in Google Scholar

[40] F. Brandt and M. Hieber, Time periodic solutions to Hibler’s sea ice model, Nonlinearity 36 (2023), no. 6, 3109–3124. 10.1088/1361-6544/accfdeSuche in Google Scholar

[41] S. Breneis, Functions of bounded variation in one and multiple dimensions, Master Thesis, Johannes Kepler Universität Linz, 2020. Suche in Google Scholar

[42] H. Brézis, Periodic solutions of nonlinear vibrating strings and duality principles, Bull. Amer. Math. Soc. (N. S.) 8 (1983), no. 3, 409–426. 10.1090/S0273-0979-1983-15105-4Suche in Google Scholar

[43] H. Bustos, P. Figueroa and M. Pinto, Poincaré–Perron problem for high order differential equations in the class of almost periodic type functions, J. Differential Equations 417 (2025), 231–259. 10.1016/j.jde.2024.11.016Suche in Google Scholar

[44] T. Caraballo and D. Cheban, Almost periodic and asymptotically almost periodic solutions of Liénard equations, Discrete Contin. Dyn. Syst. Ser. B 16 (2011), no. 3, 703–717. 10.3934/dcdsb.2011.16.703Suche in Google Scholar

[45] A. Chapouto, R. Killip and M. Vişan, Bounded solutions of KdV: Uniqueness and the loss of almost periodicity, Duke Math. J. 173 (2024), no. 7, 1227–1267. 10.1215/00127094-2023-0035Suche in Google Scholar

[46] G. E. Chatzarakis, L. H. Dmitrović and M. Pašić, Oscillation tests for difference equations with several non-monotone deviating arguments, Math. Slovaca 68 (2018), no. 5, 1083–1096. 10.1515/ms-2017-0170Suche in Google Scholar

[47] G. E. Chatzarakis, J. Manojlovic, S. Pinelas and I. P. Stavroulakis, Oscillation criteria of difference equations with several deviating arguments, Yokohama Math. J. 60 (2014), 13–31. Suche in Google Scholar

[48] A. Chávez, K. Khalil, M. Kostić and M. Pinto, Stepanov multi-dimensional almost periodic functions and applications, Filomat 37 (2023), no. 12, 3681–3713. 10.2298/FIL2312681CSuche in Google Scholar

[49] D. Cheban and Z. Liu, Periodic, quasi-periodic, almost periodic, almost automorphic, Birkhoff recurrent and Poisson stable solutions for stochastic differential equations, J. Differential Equations 269 (2020), no. 4, 3652–3685. 10.1016/j.jde.2020.03.014Suche in Google Scholar

[50] H. Chen, H. Tang and J. Sun, Periodic solutions of second-order differential equations with multiple delays, Adv. Difference Equ. 2012 (2012), Paper No. 43. 10.1186/1687-1847-2012-43Suche in Google Scholar

[51] Y. Chen, J. J. Nieto and D. O’Regan, Anti-periodic solutions for evolution equations associated with maximal monotone mappings, Appl. Math. Lett. 24 (2011), no. 3, 302–307. 10.1016/j.aml.2010.10.010Suche in Google Scholar

[52] M. Cheng and Z. Liu, Periodic, almost periodic and almost automorphic solutions for SPDEs with monotone coefficients, Discrete Contin. Dyn. Syst. Ser. B 26 (2021), no. 12, 6425–6462. 10.3934/dcdsb.2021026Suche in Google Scholar

[53] M. Cheng and Z. Liu, The second Bogolyubov theorem and global averaging principle for SPDEs with monotone coefficients, SIAM J. Math. Anal. 55 (2023), no. 2, 1100–1144. 10.1137/21M1443698Suche in Google Scholar

[54] Y. Cheng, F. Cong and H. Hua, Anti-periodic solutions for nonlinear evolution equations, Adv. Difference Equ. 2012 (2012), Paper No. 165. 10.1186/1687-1847-2012-165Suche in Google Scholar

[55] Z. Cheng and X. Cui, Positive periodic solution to an indefinite singular equation, Appl. Math. Lett. 112 (2021), Article ID 106740. 10.1016/j.aml.2020.106740Suche in Google Scholar

[56] K.-S. Chiu, Numerical-analytic successive approximation method for the investigation of periodic solutions of nonlinear integro-differential systems with piecewise constant argument of generalized type, Hacet. J. Math. Stat. 53 (2024), no. 5, 1272–1290. 10.15672/hujms.1298168Suche in Google Scholar

[57] W. Chojnacki, An analogue of the argument theorem of Bohr and its application, Studia Math. 79 (1984), no. 1, 51–59. 10.4064/sm-79-1-51-59Suche in Google Scholar

[58] J. Chu and Z. Zhang, Periodic solutions of singular differential equations with sign-changing potential, Bull. Aust. Math. Soc. 82 (2010), no. 3, 437–445. 10.1017/S0004972710001607Suche in Google Scholar

[59] K. M. Chudinov, Sharp explicit oscillation conditions for difference equations with several delays, Georgian Math. J. 28 (2021), no. 2, 207–218. 10.1515/gmj-2019-2060Suche in Google Scholar

[60] C. Corduneanu, Almost periodic solutions to nonlinear elliptic and parabolic equations, Nonlinear Anal. 7 (1983), no. 4, 357–363. 10.1016/0362-546X(83)90089-5Suche in Google Scholar

[61] D. Damanik, Schrödinger operators with dynamically defined potentials, Ergodic Theory Dynam. Systems 37 (2017), no. 6, 1681–1764. 10.1017/etds.2015.120Suche in Google Scholar

[62] D. Damanik and A. Gorodetski, An extension of the Kunz–Souillard approach to localization in one dimension and applications to almost-periodic Schrödinger operators, Adv. Math. 297 (2016), 149–173. 10.1016/j.aim.2016.04.006Suche in Google Scholar

[63] D. Damanik, M. Lukić, A. Voberg and P. Yuditskii, The Deift conjecture: A program to construct a counterexample, preprint (2021), https://arxiv.org/abs/2111.09345. Suche in Google Scholar

[64] P. Deift, Some open problems in random matrix theory and the theory of integrable systems, Integrable Systems and Random Matrices, Contemp. Math. 458, American Mathematical Society, Providence (2008), 419–430. 10.1090/conm/458/08951Suche in Google Scholar

[65] P. Deift, Some open problems in random matrix theory and the theory of integrable systems. II, SIGMA Symmetry Integrability Geom. Methods Appl. 13 (2017), Paper No. 016. Suche in Google Scholar

[66] C. R. de Oliveira, Almost periodic Schrödinger operators along interval exchange transformations, Cadernos Mat. 3 (2002), 293–304. Suche in Google Scholar

[67] J. de Vries, Elements of Topological Dynamics, Math. Appl. 257, Kluwer Academic, Dordrecht, 1993. 10.1007/978-94-015-8171-4Suche in Google Scholar

[68] T. Diagana, Almost Automorphic Type and Almost Periodic Type Functions in Abstract Spaces, Springer, Cham, 2013. 10.1007/978-3-319-00849-3Suche in Google Scholar

[69] T. Diagana and M. M. Mbaye, Square-mean almost periodic solutions to some singular stochastic differential equations, Appl. Math. Lett. 54 (2016), 48–53. 10.1016/j.aml.2015.10.013Suche in Google Scholar

[70] B. X. Dieu, S. Siegmund and V. M. Nguyen, A Katznelson–Tzafriri type theorem for almost periodic linear evolution equations, Vietnam J. Math. 43 (2015), no. 2, 403–415. 10.1007/s10013-015-0143-1Suche in Google Scholar

[71] H.-S. Ding, W.-G. Jian, N. V. Minh and G. M. N’Guérékata, Kadets type and Loomis type theorems for asymptotically almost periodic functions, J. Differential Equations 373 (2023), 389–410. 10.1016/j.jde.2023.07.019Suche in Google Scholar

[72] R. Doss, On Riemann integrability and almost periodic functions, Compos. Math. 12 (1956), 271–283. Suche in Google Scholar

[73] N. Drisi and B. Es-sebbar, Almost automorphic solutions to logistic equations with discrete and continuous delay, C. R. Math. Acad. Sci. Paris 355 (2017), no. 12, 1208–1214. 10.1016/j.crma.2017.11.004Suche in Google Scholar

[74] A. S. Džafarov and G. M. Gasanov, Almost periodic functions with respect to the Hausdorff metric, and their properties (in Russian), Izv. Akad. Nauk Azerbaĭdžan. SSR Ser. Fiz.-Tehn. Mat. Nauk (1977), no. 1, 57–62. Suche in Google Scholar

[75] A. Dzurnak and A. B. Mingarelli, Sturm–Liouville equations with Besicovitch almost-periodicity, Proc. Amer. Math. Soc. 106 (1989), no. 3, 647–653. 10.1090/S0002-9939-1989-0938910-4Suche in Google Scholar

[76] T. Eisner, B. Farkas, M. Haase and R. Nagel, Operator Theoretic Aspects of Ergodic Theory, Grad. Texts in Math. 272, Springer, Cham, 2015. 10.1007/978-3-319-16898-2Suche in Google Scholar

[77] L. E. El’sgol’ts and S. B. Norkin, Introduction to the Theory of Differential Equations with Deviating Argument, Nauka, Moscow, 1971. Suche in Google Scholar

[78] L. C. Evans and R. F. Gariepy, Measure Theory and Fine Properties of Functions, Stud. Adv. Math., CRC Press, Boca Raton, 1992. Suche in Google Scholar

[79] M. Faheem and M. Rama Mohana Rao, Functional-differential equations of delay type and nonlinear evolution in L p -spaces, J. Math. Anal. Appl. 123 (1987), no. 1, 73–103. 10.1016/0022-247X(87)90294-0Suche in Google Scholar

[80] Z. Feng, Y. Wang and X. Ma, Asymptotically almost periodic solutions for certain differential equations with piecewise constant arguments, Adv. Difference Equ. 2020 (2020), Paper No. 242. 10.1186/s13662-020-02699-6Suche in Google Scholar

[81] P. Figueroa and M. Pinto, Poincaré’s problem in the class of almost periodic type functions, Bull. Belg. Math. Soc. Simon Stevin 22 (2015), no. 2, 177–198. 10.36045/bbms/1432840857Suche in Google Scholar

[82] A. M. Fink, Almost Periodic Differential Equations, Lecture Notes in Math. 377, Springer, Berlin, 1974. 10.1007/BFb0070324Suche in Google Scholar

[83] R. A. Fisher, The advance of advantageous genes, Ann. Eugenics 7 (1937), 335–369. 10.1111/j.1469-1809.1937.tb02153.xSuche in Google Scholar

[84] H. Frid, Decay of almost periodic solutions of conservation laws, Arch. Ration. Mech. Anal. 161 (2002), no. 1, 43–64. 10.1007/s002050100169Suche in Google Scholar

[85] G. Fuhrmann and D. Kwietniak, On tameness of almost automorphic dynamical systems for general groups, Bull. Lond. Math. Soc. 52 (2020), no. 1, 24–42. 10.1112/blms.12304Suche in Google Scholar

[86] R. E. Gaines and J. L. Mawhin, Coincidence Degree, and Nonlinear Differential Equations, Lecture Notes in Math. 568, Springer, Berlin, 1977. 10.1007/BFb0089537Suche in Google Scholar

[87] F. García-Ramos, T. Jäger and X. Ye, Mean equicontinuity, almost automorphy and regularity, Israel J. Math. 243 (2021), no. 1, 155–183. 10.1007/s11856-021-2157-6Suche in Google Scholar

[88] E. Glasner, Enveloping semigroups in topological dynamics, Topology Appl. 154 (2007), no. 11, 2344–2363. 10.1016/j.topol.2007.03.009Suche in Google Scholar

[89] W. H. Gottschalk and G. A. Hedlund, Topological Dynamics, Amer. Math. Soc. Colloq. Publ. 36, American Mathematical Society, Providence, 1955. Suche in Google Scholar

[90] K. Geba and W. Marzantowicz, Global bifurcation of periodic solutions, Topol. Methods Nonlinear Anal. 1 (1993), no. 1, 67–93. 10.12775/TMNA.1993.008Suche in Google Scholar

[91] R. B. Grafton, A periodicity theorem for autonomous functional differential equations, J. Differential Equations 6 (1969), 87–109. 10.1016/0022-0396(69)90119-3Suche in Google Scholar

[92] K.-G. Grosse-Erdmann and A. Peris Manguillot, Linear Chaos, Universitext, Springer, London, 2011. 10.1007/978-1-4471-2170-1Suche in Google Scholar

[93] H. Hahn, Theorie der Reellen Funktionen. 1, Springer, Berlin, 1921. 10.1007/978-3-642-52624-4_1Suche in Google Scholar

[94] R. Hakl, E. Trofimchuk and S. Trofimchuk, Periodic-type solutions for differential equations with positively homogeneous functionals, J. Math. Sci. (N. Y.) 274 (2023), no. 1, 126–141. 10.1007/s10958-023-06575-ySuche in Google Scholar

[95] G. H. Hardy, On double Fourier series and especially those which represent the double zeta-function with real and incommensurable parameters, Quart. J. Math. 37 (1905), 53–79. Suche in Google Scholar

[96] B. Hasselblatt, Anatole Katok, Ergodic Theory Dynam. Systems 42 (2022), no. 2, 321–388. 10.1017/etds.2021.72Suche in Google Scholar

[97] L. Haupt and T. Jäger, Construction of smooth isomorphic and finite-to-one extensions of irrational rotations which are not almost automorphic, Ergodic Theory Dynam. Systems 45 (2025), no. 4, 1224–1245. 10.1017/etds.2024.70Suche in Google Scholar

[98] M. L. Hbid and R. Qesmi, Periodic solutions for functional differential equations with periodic delay close to zero, Electron. J. Differential Equations 2006 (2006), Paper No. 141. Suche in Google Scholar

[99] J. He, F. Kong, J. J. Nieto and H. Qiu, Globally exponential stability of piecewise pseudo almost periodic solutions for neutral differential equations with impulses and delays, Qual. Theory Dyn. Syst. 21 (2022), no. 2, Paper No. 48. 10.1007/s12346-022-00578-xSuche in Google Scholar

[100] W. He, J. Yin and Z. Zhou, On quasi-weakly almost periodic points, Sci. China Math. 56 (2013), no. 3, 597–606. 10.1007/s11425-012-4560-2Suche in Google Scholar

[101] P. Hess, Periodic-Parabolic Boundary Value Problems and Positivity, Pitman Res. Notes Math. Ser. 247, Longman Scientific & Technical, Harlow, 1991. Suche in Google Scholar

[102] M. Hieber, A. Mahalov and R. Takada, Time periodic and almost time periodic solutions to rotating stratified fluids subject to large forces, J. Differential Equations 266 (2019), no. 2–3, 977–1002. 10.1016/j.jde.2018.07.067Suche in Google Scholar

[103] M. Hieber and T. H. Nguyen, Stability and periodicity of solutions to the Oldroyd-B model on exterior domains, Rend. Istit. Mat. Univ. Trieste 52 (2020), 113–129. Suche in Google Scholar

[104] M. Hieber and C. Stinner, Strong time periodic solutions to Keller–Segel systems: An approach by the quasilinear Arendt–Bu theorem, J. Differential Equations 269 (2020), no. 2, 1636–1655. 10.1016/j.jde.2020.01.020Suche in Google Scholar

[105] N. Hua, The fixed point theory and the existence of the periodic solution on a nonlinear differential equation, J. Appl. Math. 2018 (2018), Article ID 6725989. 10.1155/2018/6725989Suche in Google Scholar

[106] T. Iwamiya, Global existence of mild solutions to semilinear differential equations in Banach spaces, Hiroshima Math. J. 16 (1986), no. 3, 499–530. 10.32917/hmj/1206130305Suche in Google Scholar

[107] D. Jackson, Über die Genauigkeit der Annäherung stetiger Funktionen durch ganze rationale Funktionen gegebenen Grades und trigonometrische Summen gegebener Ordnung, Ph. D. Thesis, University of Göttingen, 1911. Suche in Google Scholar

[108] K. Jacobs and M. Keane, 0 - 1 -sequences of Toeplitz type, Z. Wahrscheinlichkeitstheorie Verw. Geb. 13 (1969), 123–131. 10.1007/BF00537017Suche in Google Scholar

[109] J. Jezierski and W. Marzantowicz, Homotopy Methods in Topological Fixed and Periodic Points Theory, Topol. Fixed Point Theory Appl. 3, Springer, Dordrecht, 2006. 10.1007/1-4020-3931-XSuche in Google Scholar

[110] D. Ji, L. Yang and J. Zhang, Almost periodic functions on Hausdorff almost periodic time scales, Adv. Difference Equ. 2017 (2017), Paper No. 103. 10.1186/s13662-017-1159-5Suche in Google Scholar

[111] M. A. Johnson, P. Noble, L. M. Rodrigues and K. Zumbrun, Nonlocalized modulation of periodic reaction diffusion waves: Nonlinear stability, Arch. Ration. Mech. Anal. 207 (2013), no. 2, 693–715. 10.1007/s00205-012-0573-9Suche in Google Scholar

[112] M. A. Johnson, P. Noble, L. M. Rodrigues and K. Zumbrun, Nonlocalized modulation of periodic reaction diffusion waves: The Whitham equation, Arch. Ration. Mech. Anal. 207 (2013), no. 2, 669–692. 10.1007/s00205-012-0572-xSuche in Google Scholar

[113] R. Johnson and Y. Yi, Hopf bifurcation from nonperiodic solutions of differential equations. II, J. Differential Equations 107 (1994), no. 2, 310–340. 10.1006/jdeq.1994.1015Suche in Google Scholar

[114] R. A. Johnson, On a Floquet theory for almost-periodic, two-dimensional linear systems, J. Differential Equations 37 (1980), no. 2, 184–205. 10.1016/0022-0396(80)90094-7Suche in Google Scholar

[115] R. A. Johnson, Two-dimensional, almost periodic linear systems with proximal and recurrent behavior, Proc. Amer. Math. Soc. 82 (1981), no. 3, 417–422. 10.1090/S0002-9939-1981-0612732-9Suche in Google Scholar

[116] R. A. Johnson, On almost-periodic linear differential systems of Millionshchikov and Vinograd, J. Math. Anal. Appl. 85 (1982), no. 2, 452–460. 10.1016/0022-247X(82)90011-7Suche in Google Scholar

[117] R. A. Johnson, Hopf bifurcation from nonperiodic solutions of differential equations. I. Linear theory, J. Dynam. Differential Equations 1 (1989), no. 2, 179–198. 10.1007/BF01047830Suche in Google Scholar

[118] G. A. Kamenskii and A. L. Skubachevskii, Theory of Functional Differential Equations, Mosc. Aviats. Inst., Moscow, 1992. Suche in Google Scholar

[119] M. Keane, Generalized Morse sequences, Z. Wahrscheinlichkeitstheorie Verw. Geb. 10 (1968), 335–353. 10.1007/BF00531855Suche in Google Scholar

[120] J. Knezević-Miljanović, Periodic solutions of nonlinear differential equations, Adv. Dyn. Syst. Appl. 7 (2012), no. 1, 89–93. Suche in Google Scholar

[121] A. N. Kolmogorov, I. G. Petrovsky and N. S. Piskunov, Etude de l’équation de la diffusion avec croissance de la quantité de matière et son application à un problème biologique, Bulle. Univ. d’Etat à Moscou (1937), 1–26. Suche in Google Scholar

[122] J. V. Komlenko and E. L. Tonkov, The multipliers of a linear periodic differential equation with deviating argument (in Russian), Sibirsk. Mat. Ž. 15 (1974), 835–844, 958. 10.1007/BF00967434Suche in Google Scholar

[123] M. Kostić, Almost Periodic and Almost Automorphic Solutions to Integro-Differential Equations, De Gruyter, Berlin, 2019. 10.1515/9783110641851Suche in Google Scholar

[124] M. Kostić, Abstract Degenerate Volterra Integro-Differential Equations, Mathematical Institute SANU, Belgrade, 2020. Suche in Google Scholar

[125] M. Kostić, Chaos for Linear Operators and Abstract Differential Equations, Nova Science, New York, 2020. 10.52305/IDIC2486Suche in Google Scholar

[126] M. Kostić, Selected Topics in Almost Periodicity, De Gruyter Stud. Math. 84, De Gruyter, Berlin, 2022. 10.1515/9783110763522Suche in Google Scholar

[127] M. Kostić, Metrical Almost Periodicity and Applications to Integro-Differential Equations, De Gruyter Stud. Math. 95, De Gruyter, Berlin, 2023. 10.1515/9783111233871Suche in Google Scholar

[128] M. Kostić, Almost Periodic Type Solutions to Integro-Differential-Difference Equations, De Gruyter, Berlin, 2025. 10.1515/9783111689746Suche in Google Scholar

[129] P. Krejčí, Otto Vejvoda passed away, Appl. Math. 54 (2009), no. 4, 377–378. 10.1007/s10492-009-0023-7Suche in Google Scholar

[130] J. Kurzweil and O. Vejvoda, On the periodic and almost periodic solutions of a system of ordinary differential equations, Czechoslovak Math. J. 5(80) (1955), 362–370. 10.21136/CMJ.1955.100152Suche in Google Scholar

[131] A. C. Lazer and S. Solimini, On periodic solutions of nonlinear differential equations with singularities, Proc. Amer. Math. Soc. 99 (1987), no. 1, 109–114. 10.1090/S0002-9939-1987-0866438-7Suche in Google Scholar

[132] B. M. Levitan, Almost Periodic Functions (in Russian), Fizmatgiz, Moscow, 1953. Suche in Google Scholar

[133] B. M. Levitan and V. V. Zhikov, Almost Periodic Functions and Differential Equations, Cambridge University, Cambridge, 1982. Suche in Google Scholar

[134] Y. Li and S. Shen, Compact almost automorphic function on time scales and its application, Qual. Theory Dyn. Syst. 20 (2021), no. 3, Paper No. 86. 10.1007/s12346-021-00522-5Suche in Google Scholar

[135] J. Liang, Y. Liu and C. Gao, Almost periodic solution to singular systems, Chinese Sci. Bull. 43 (1998), no. 8, 698–700. 10.1007/BF02883581Suche in Google Scholar

[136] T. Liang, Y. Q. Yang, Y. Liu and L. Li, Existence and global exponential stability of almost periodic solutions to Cohen-Grossberg neural networks with distributed delays on time scales, Neurocomputing 123 (2014), 207–215. 10.1016/j.neucom.2013.07.010Suche in Google Scholar

[137] Z. Liang, X. Zhang and S. Li, Periodic solutions of an indefinite singular planar differential system, Mediterr. J. Math. 20 (2023), no. 1, Paper No. 41. 10.1007/s00009-022-02237-6Suche in Google Scholar

[138] Z. Liang, X. Zhang, S. Li and Z. Zhou, Periodic solutions of a class of indefinite singular differential equations, Electron. Res. Arch. 31 (2023), no. 4, 2139–2148. 10.3934/era.2023110Suche in Google Scholar

[139] Y. Liu, Multiplicity of positive almost periodic solutions and local asymptotical stability for a kind of time-varying fishing model with harvesting term, Engineering Letters 28 (2020), no. 4, Article ID EL/28/4/31. Suche in Google Scholar

[140] Z. Liu and W. Wang, Favard separation method for almost periodic stochastic differential equations, J. Differential Equations 260 (2016), no. 11, 8109–8136. 10.1016/j.jde.2016.02.019Suche in Google Scholar

[141] N. T. Loan, V. A. N. Thi, T. V. Thuy and P. T. Xuan, Periodic solutions of the parabolic-elliptic Keller–Segel system on whole spaces, Math. Nachr. 297 (2024), no. 8, 3003–3023. 10.1002/mana.202300311Suche in Google Scholar

[142] N. T. Loan and P. T. Xuan, Almost periodic solutions of the parabolic-elliptic Keller–Segel system on the whole space, Arch. Math. (Basel) 123 (2024), no. 4, 431–446. 10.1007/s00013-024-02023-8Suche in Google Scholar

[143] M. E. Lord and A. R. Mitchell, A new approach to the method of nonlinear variation of parameters, Appl. Math. Comput. 4 (1978), no. 2, 95–105. 10.1016/0096-3003(78)90014-0Suche in Google Scholar

[144] S. Lu, A new result on the existence of periodic solutions for Liénard equations with a singularity of repulsive type, J. Inequal. Appl. 2017 (2017), Paper No. 37. 10.1186/s13660-016-1285-8Suche in Google Scholar PubMed PubMed Central

[145] A. Lunardi, Interpolation Theory, Appunti. Sc. Norm. Super. Pisa (N. S.) 16, Edizioni della Normale, Pisa, 2018. Suche in Google Scholar

[146] J.-H. Mai and W.-H. Sun, Almost periodic points and minimal sets in ω-regular spaces, Topology Appl. 154 (2007), no. 15, 2873–2879. 10.1016/j.topol.2007.06.007Suche in Google Scholar

[147] M. Maqbul, Almost periodic solutions for a class of nonlinear Duffing system with time-varying coefficients and Stepanov-almost periodic forcing terms, Nonlinear Dyn. Syst. Theory 20 (2020), no. 5, 512–522. Suche in Google Scholar

[148] N. G. Markley and M. E. Paul, Almost automorphic symbolic minimal sets without unique ergodicity, Israel J. Math. 34 (1979), no. 3, 259–272. 10.1007/BF02760887Suche in Google Scholar

[149] J. C. Martin, Substitution minimal flows, Bull. Amer. Math. Soc. 77 (1971), 610–612. 10.1090/S0002-9904-1971-12771-4Suche in Google Scholar

[150] P. J. McKenna, On solutions of a nonlinear wave question when the ratio of the period to the length of the interval is irrational, Proc. Amer. Math. Soc. 93 (1985), no. 1, 59–64. 10.1090/S0002-9939-1985-0766527-XSuche in Google Scholar

[151] M. McKibben, Discovering Evolution Equations with Applications. Vol. 1 – Deterministic Equations, Chapman and Hall/CRC, Boca Raton, 2010. 10.1201/9781420092097Suche in Google Scholar

[152] D. McMahon and T. S. Wu, On weak mixing and local almost periodicity, Duke Math. J. 39 (1972), 333–343. 10.1215/S0012-7094-72-03940-3Suche in Google Scholar

[153] B. Meknani, J. Zhang and T. Abdelhamid, Pseudo-almost periodic C 0 solutions to the evolution equations with nonlocal initial conditions, Appl. Anal. 102 (2023), no. 4, 1027–1037. 10.1080/00036811.2021.1969368Suche in Google Scholar

[154] F. H. Meng and W. H. Qiu, Reducibility for a class of two-dimensional almost periodic system with small perturbation, Adv. Pure Math. 11 (2021), 950–962. 10.4236/apm.2021.1112061Suche in Google Scholar

[155] N. V. Minh, H. Matsunaga, N. D. Huy and V. T. Luong, A Katznelson–Tzafriri type theorem for difference equations and applications, Proc. Amer. Math. Soc. 150 (2022), no. 3, 1105–1114. 10.1090/proc/15722Suche in Google Scholar

[156] N. V. Minh, H. Matsunaga, N. D. Huy and V. T. Luong, A spectral theory of polynomially bounded sequences and applications to the asymptotic behavior of discrete systems, Funkcial. Ekvac. 65 (2022), no. 3, 261–285. 10.1619/fesi.65.261Suche in Google Scholar

[157] C. A. Morales, Equicontinuity on semi-locally connected spaces, Topology Appl. 198 (2016), 101–106. 10.1016/j.topol.2015.11.011Suche in Google Scholar

[158] A. B. Muravnik, Functional-differential parabolic equations: Integral representations and qualitative properties of the solutions of the Cauchy equation, J. Math. Sci. (N. Y.) 216 (2016), 354–496. 10.1007/s10958-016-2904-0Suche in Google Scholar

[159] A. B. Muravnik, Elliptic differential-difference equations in the half-space, Mat. Notes 67 (2020), 727–732. 10.1134/S0001434620110115Suche in Google Scholar

[160] A. B. Muravnik, Half-plane differential-difference elliptic problems with general-kind nonlocal potentials, Complex Var. Elliptic Equ. 67 (2022), no. 5, 1101–1120. 10.1080/17476933.2020.1857372Suche in Google Scholar

[161] A. B. Muravnik, Differential-difference elliptic equations with nonlocal potentials in half-spaces, Mathematics 11 (2023), 10.3390/math11122698. 10.3390/math11122698Suche in Google Scholar

[162] A. D. Myshkis, Linear Differential Equations with Delayed Argument (in Russian), Izdat. “Nauka”, Moscow, 1972. Suche in Google Scholar

[163] G. Nadin, The principal eigenvalue of a space-time periodic parabolic operator, Ann. Mat. Pura Appl. (4) 188 (2009), no. 2, 269–295. 10.1007/s10231-008-0075-4Suche in Google Scholar

[164] G. Nadin, Traveling fronts in space-time periodic media, J. Math. Pures Appl. (9) 92 (2009), no. 3, 232–262. 10.1016/j.matpur.2009.04.002Suche in Google Scholar

[165] T. T. Ngoc and P. T. Xuan, Existence and stability of almost periodic solutions of Boussinesq systems in Morrey-type spaces, preprint (2024), https://www.researchgate.net/publication/381614173. 10.1007/s00574-024-00423-6Suche in Google Scholar

[166] G. M. N’Guerekata, Almost Automorphic and Almost Periodic Functions in Abstract Spaces, Kluwer Academic, Dordrecht, 2001. 10.1007/978-1-4757-4482-8Suche in Google Scholar

[167] T. V. A. Nguyen, Periodic solutions to differential variational inequalities of parabolic-elliptic type, Taiwanese J. Math. 24 (2020), no. 6, 1497–1527. 10.11650/tjm/200301Suche in Google Scholar

[168] G. C. O’Brien, Almost periodic and quasi-periodic solutions of differential equations, Ph.D. Thesis, The Australian National University, Canberra, 1972. 10.1017/S0004972700045342Suche in Google Scholar

[169] S. Oharu and T. Takahashi, Characterization of nonlinear semigroups associated with semilinear evolution equations, Trans. Amer. Math. Soc. 311 (1989), no. 2, 593–619. 10.2307/2001143Suche in Google Scholar

[170] J.-S. Pang and D. E. Stewart, Differential variational inequalities, Math. Program. 113 (2008), no. 2, 345–424. 10.1007/s10107-006-0052-xSuche in Google Scholar

[171] A. A. Pankov, Bounded and Almost Periodic Solutions of Nonlinear Operator Differential Equations, Math. Appl. (Soviet Series) 55, Kluwer Academic, Dordrecht, 1990. 10.1007/978-94-011-9682-6Suche in Google Scholar

[172] N. S. Papageorgiou, V. D. Rădulescu and D. D. Repovš, Periodic solutions for a class of evolution inclusions, Comput. Math. Appl. 75 (2018), no. 8, 3047–3065. 10.1016/j.camwa.2018.01.031Suche in Google Scholar

[173] M. E. Paul, Construction of almost automorphic symbolic minimal flows, General. Topol. Appl. 6 (1976), no. 1, 45–56. 10.1016/0016-660X(76)90007-6Suche in Google Scholar

[174] A. P. Petukhov, The space of almost periodic functions with the Hausdorff metric, Mat. Sb. 185 (1994), no. 3, 69–92. Suche in Google Scholar

[175] J. Pierpont, Lectures on the Theory of Functions of Real Variables, Dover Publications, New York, 1959. Suche in Google Scholar

[176] M. Pinto and S. Trofimchuk, Stability and existence of multiple periodic solutions for a quasilinear differential equation with maxima, Proc. Roy. Soc. Edinburgh Sect. A 130 (2000), no. 5, 1103–1118. 10.1017/S0308210500000597Suche in Google Scholar

[177] H. Poincaré, Les Méthodes nouvelles de la Mécanique Céleste, Gauthier-Villars, Paris, 1982. Suche in Google Scholar

[178] J. Puig, Reducibility of linear equations with quasi-periodic coefficients. A survey, Research Report MP-ARC-2002-246, Texas University, 2002. Suche in Google Scholar

[179] P. H. Rabinowitz, Minimax Methods in Critical Point Theory with Applications to Differential Equations, CBMS Reg. Conf. Ser. Math. 65, American Mathematical Society, Providence, 1986. 10.1090/cbms/065Suche in Google Scholar

[180] S. Radchenko, V. Samoilenko and P. Samusenko, Asymptotic solutions of singularly perturbed linear differential-algebraic equations with periodic coefficients, Mat. Stud. 59 (2023), no. 2, 187–200. 10.30970/ms.59.2.187-200Suche in Google Scholar

[181] D. Rojas, Resonance of bounded isochronous oscillators, Nonlinear Anal. 192 (2020), Article ID 111680. 10.1016/j.na.2019.111680Suche in Google Scholar

[182] D. Rojas and P. J. Torres, Periodic bouncing solutions of the Lazer–Solimini equation with weak repulsive singularity, Nonlinear Anal. Real World Appl. 64 (2022), Article ID 103441. 10.1016/j.nonrwa.2021.103441Suche in Google Scholar

[183] A. N. Ronto, On periodic solutions of systems with “maxima”, Dopov. Nats. Akad. Nauk Ukr. Mat. Prirodozn. Tekh. Nauki 12 (1999), 27–31. Suche in Google Scholar

[184] L. T. Sac and P. T. Xuan, Well-posedness and stability for a class of solutions of semi-linear diffusion equations with rough coefficients, Filomat 38 (2024), no. 31, 10893–10911. 10.2298/FIL2431893SSuche in Google Scholar

[185] A. M. Samoĭlenko and N. A. Perestyuk, Impulsive Differential Equations, World Scientific, Singapore, 1995. 10.1142/9789812798664Suche in Google Scholar

[186] G. Sell, W. Shen and Y. Yi, Topological dynamics and differential equations, Topological dynamics and Applications (Minneapolis 1995), Contemp. Math. 215, American Mathematical Society, Providence (1998), 279–297. 10.1090/conm/215/02948Suche in Google Scholar

[187] J. M. Sepulcre and T. Vidal, Bohr’s equivalence relation in the space of Besicovitch almost periodic functions, Ramanujan J. 49 (2019), no. 3, 625–639. 10.1007/s11139-018-0022-ySuche in Google Scholar

[188] A. S. Serdyuk and A. L. Shidlich, Direct and inverse theorems on the approximation of almost periodic functions in Besicovitch–Stepanets spaces, Carpathian Math. Publ. 13 (2021), no. 3, 687–700. 10.15330/cmp.13.3.687-700Suche in Google Scholar

[189] W. Shen, Travelling waves in time almost periodic structures governed by bistable nonlinearities. I. Stability and uniqueness, J. Differential Equations 159 (1999), no. 1, 1–54. 10.1006/jdeq.1999.3651Suche in Google Scholar

[190] W. Shen, Travelling waves in time almost periodic structures governed by bistable nonlinearities. II. Existence, J. Differential Equations 159 (1999), no. 1, 55–101. 10.1006/jdeq.1999.3652Suche in Google Scholar

[191] S. Sivaji Ganesh and V. Tewary, Bloch wave approach to almost periodic homogenization and approximations of effective coefficients, Discrete Contin. Dyn. Syst. Ser. B 27 (2022), no. 4, 1989–2024. 10.3934/dcdsb.2021119Suche in Google Scholar

[192] A. L. Skubachevskii, Elliptic Functional-Differential Equations and Applications, Oper. Theory Adv. Appl. 91, Birkhäuser, Basel, 1997. 10.1007/978-3-0348-9033-5_3Suche in Google Scholar

[193] Q. Song and J. Cao, Stability analysis of Cohen–Grossberg neural network with both time-varying and continuously distributed delays, J. Comput. Appl. Math. 197 (2006), no. 1, 188–203. 10.1016/j.cam.2005.10.029Suche in Google Scholar

[194] G. T. Stamov, Almost Periodic Solutions of Impulsive Differential Equations, Lecture Notes in Math. 2047, Springer, Heidelberg, 2012. 10.1007/978-3-642-27546-3Suche in Google Scholar

[195] V. Štastnová and O. Vejvoda, Periodic solutions of the first boundary value problem for a linear and weakly nonlinear heat equation, Apl. Mat. 13 (1968), 466–477. 10.21136/AM.1968.103196Suche in Google Scholar

[196] W. Stepanoff, Über einige Verallgemeinerungen der fast periodischen Funktionen, Math. Ann. 95 (1926), no. 1, 473–498. 10.1007/BF01206623Suche in Google Scholar

[197] S. Stoiński, H-almost periodic functions, Funct. Approx. Comment. Math. 1 (1974), 113–122. Suche in Google Scholar

[198] S. Stoiński, A connection between H-almost periodic functions and almost periodic functions of other types, Funct. Approx. Comment. Math. 3 (1976), 205–223. Suche in Google Scholar

[199] S. Stoiński, On unbounded almost periodic functions in Hausdorff metric, Comment. Math. 53 (2013), no. 1, 17–22. 10.14708/cm.v53i1.769Suche in Google Scholar

[200] M. Struwe, Variational Methods, 2nd ed., Ergeb. Math. Grenzgeb. (3) 34, Springer, Berlin, 1996. 10.1007/978-3-662-03212-1Suche in Google Scholar

[201] M. A. Šubin, Almost periodic functions and partial differential operators, Russian Math. Surveys 33 (1978), 1–52. 10.1070/RM1978v033n02ABEH002303Suche in Google Scholar

[202] M. Toda, Vibration of a chain with nonlinear interaction, J. Phys. Soc. Japan 22 (1967), 431–436. 10.1143/JPSJ.22.431Suche in Google Scholar

[203] H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, North-Holland Math. Libr. 18, North-Holland, Amsterdam, 1978. Suche in Google Scholar

[204] O. Trofymchuk, E. Liz and S. Trofimchuk, The peak-end rule and its dynamic realization through differential equations with maxima, Nonlinearity 36 (2023), no. 1, 507–536. 10.1088/1361-6544/aca50dSuche in Google Scholar

[205] O. Vejvoda, On the existence and stability of the periodic solution of the second kind of a certain mechanical system, Czechoslovak Math. J. 9(84) (1959), 390–415. 10.21136/CMJ.1959.100364Suche in Google Scholar

[206] O. Vejvoda, Partial Differential Equations: Time-Periodic Solutions, Martinus Nijhoff, Leiden, 1981. 10.1007/978-94-009-7672-6Suche in Google Scholar

[207] G. Vitali, Sui gruppi di punti e sulle funzioni di variabili real, Atti Accad. Sci. Torino 43 (1908), 75–92. Suche in Google Scholar

[208] V. V. Vlasov and D. A. Medvedev, Functional-differential equations in Sobolev spaces and related problems in spectral theory, J. Math. Sci. (N.Y.) 164 (2010), 659–841. 10.1007/s10958-010-9768-5Suche in Google Scholar

[209] I. I. Vrabie, Compactness Methods for Nonlinear Evolutions, CRC Press, Boca Raton, 1995. Suche in Google Scholar

[210] I. I. Vrabie, Almost periodic solutions for nonlinear delay evolutions with nonlocal initial conditions, J. Evol. Equ. 13 (2013), no. 3, 693–714. 10.1007/s00028-013-0198-ySuche in Google Scholar

[211] I. I. Vrabie, Delay evolution equations with mixed nonlocal plus local initial conditions, Commun. Contemp. Math. 17 (2015), no. 2, Article ID 1350035. 10.1142/S0219199713500351Suche in Google Scholar

[212] P. Walters, An Introduction to Ergodic Theory, Grad. Texts in Math. 79, Springer, New York, 1982. 10.1007/978-1-4612-5775-2Suche in Google Scholar

[213] L. Wang and M. Yu, Favard’s theorem of piecewise continuous almost periodic functions and its application, J. Math. Anal. Appl. 413 (2014), no. 1, 35–46. 10.1016/j.jmaa.2013.11.029Suche in Google Scholar

[214] J. R. Ward, Jr., Periodic solutions of ordinary differential equations with bounded nonlinearities, Topol. Methods Nonlinear Anal. 19 (2002), no. 2, 275–282. 10.12775/TMNA.2002.014Suche in Google Scholar

[215] M. Ważewska-Czyżewska and A. Lasota, Mathematical problems of the dynamics of a system of red blood cells, Ann. Polish Ser. I 17 (1988), 23–40. Suche in Google Scholar

[216] G. F. Webb, Continuous nonlinear perturbations of linear accretive operators in Banach spaces, J. Funct. Anal. 10 (1972), 191–203. 10.1016/0022-1236(72)90048-1Suche in Google Scholar

[217] F. H. Wong and C. C. Yeh, An oscillation criterion for Sturm–Liouville equations with Besicovitch almost-periodic coefficients, Hiroshima Math. J. 21 (1991), no. 3, 521–528. 10.32917/hmj/1206128718Suche in Google Scholar

[218] X. Xing, Positive periodic solution for second-order singular semipositone differential equations, Abstr. Appl. Anal. 2013 (2013), Article ID 310469. 10.1155/2013/310469Suche in Google Scholar

[219] J. C. Xiong, Set of almost periodic points of a continuous self-map of an interval, Acta Math. Sinica (N. S.) 2 (1986), no. 1, 73–77. 10.1007/BF02568524Suche in Google Scholar

[220] X. Xue and Y. Cheng, Existence of periodic solutions of nonlinear evolution inclusions in Banach spaces, Nonlinear Anal. Real World Appl. 11 (2010), no. 1, 459–471. 10.1016/j.nonrwa.2008.11.020Suche in Google Scholar

[221] L. Ye and Y. Liu, Pseudo-almost periodic C 0 -solution for evolution inclusion with mixed nonlocal plus local initial conditions, Hacet. J. Math. Stat. 52 (2023), no. 6, 1480–1491. 10.15672/hujms.1143058Suche in Google Scholar

[222] J. You, Quantitative almost reducibility and its applications, Proceedings of the International Congress of Mathematicians—Rio de Janeiro 2018. Vol. III. Invited Lectures, World Scientific, Hackensack (2018), 2113–2135. 10.1142/9789813272880_0132Suche in Google Scholar

[223] R. Yuan, Almost periodic solutions of a class of singularly perturbed differential equations with piecewise constant argument, Nonlinear Anal. 37 (1999), no. 7, 841–859. 10.1016/S0362-546X(98)00076-5Suche in Google Scholar

[224] R. Yuan, On the almost periodic solution of a class of singularly perturbed differential equations with piecewise constant argument, Internat. J. Qual. Theory Diff. Equ. Appl. 2 (2008), 69–100. Suche in Google Scholar

[225] S. Zaidman, Almost-Periodic Functions in Abstract Spaces, Res. Notes Math. 126, Pitman, Boston, 1985. Suche in Google Scholar

[226] N. V. Zaitseva, On global classical solutions of hyperbolic differential-difference equations, Dokl. Math. 101 (2020), no. 2, 115–116. 10.1134/S1064562420020246Suche in Google Scholar

[227] N. V. Zaitseva, Classical solutions of hyperbolic differential-difference equations in a half-space, Differ. Equ. 57 (2021), no. 12, 1629–1639. 10.1134/S0012266121120090Suche in Google Scholar

[228] N. V. Zaitseva, Classical solutions of hyperbolic differential-difference equations with several nonlocal terms, Lobachevskii J. Math. 42 (2021), no. 1, 231–236. 10.1134/S1995080221010285Suche in Google Scholar

[229] N. V. Zaitseva, Classical solutions of hyperbolic equations with nonlocal potentials, Dokl. Math. 103 (2021), no. 3, 127–129. 10.1134/S1064562421030157Suche in Google Scholar

[230] N. V. Zaitseva, Classical solutions of a multidimensional hyperbolic differential-difference equation with shifts of various directions in the potentials, Math. Notes 112 (2022), 872–880. 10.1134/S0001434622110219Suche in Google Scholar

[231] N. V. Zaitseva, Mixed problems with integral conditions for hyperbolic equations with the Bessel operator, Differ. Equ. 59 (2023), no. 1, S1–S72. 10.1134/S00122661230130013Suche in Google Scholar

[232] S. F. Zakharin and I. O. Parasyuk, Generalized and classical almost periodic solutions of Lagrangian systems, Funkcial. Ekvac. 42 (1999), no. 3, 325–338. Suche in Google Scholar