Boundedness and almost periodicity of solutions of linear differential systems

References

[1] AHMAD, S. — TINEO, A.: Almost periodic solutions of second order systems, Appl. Anal. 63 (1996), 389–395.10.1080/00036819608840516Suche in Google Scholar

[2] BERGER, M. — CHEN, Y.: Forced quasiperiodic and almost periodic solutions for nonlinear systems, Nonlinear Anal. 21 (1993), 949–965.10.1016/0362-546X(93)90118-CSuche in Google Scholar

[3] BESICOVITCH, A. S.: Almost Periodic Functions, Cambridge University Press, Cambridge, 1932.Suche in Google Scholar

[4] BOCHNER, S.: Curvature and Betti Numbers in Real and Complex Vector- Bundles, Universita di Torino, Rendiconti del Seminario Matematico 15, 1955–1956.Suche in Google Scholar

[5] BOCHNER, S.: A new approach to almost periodicity, Proc. Nat. Ac. Sc. USA 48 (1962), 195–205.10.1073/pnas.48.12.2039Suche in Google Scholar PubMed PubMed Central

[6] BOHR, H.: Almost Periodic Functions, Chelsea, New York, 1956.Suche in Google Scholar

[7] BOHR, H.: Zur Theorie der fastperiodischen Funktionen, I. Eine Verallgemeinerung der Theorie der Fourierreihen, Acta Math. 45 (1925), 29–127.10.1007/BF02395468Suche in Google Scholar

[8] BOHR, H.: Zur Theorie der fastperiodischen Funktionen, II. Eine Verallgemeine-rung der Theorie der Fourierreihen, Acta Math. 46 (1925), 101–204.10.1007/BF02543859Suche in Google Scholar

[9] BOHR, H.: Zur Theorie der fastperiodischen Funktionen, III. Eine Verallgemeine-rung der Theorie der Fourierreihen, Acta Math. 47 (1926), 237–281.10.1007/BF02543846Suche in Google Scholar

[10] BOHR, H. — NEUGEBAUER, O.: ¨ Uber lineare Differentialgleichungen mit konstanten Koeffizienten und fast-periodischer rechter Seite. Nachrichten von der Gesellschaft der Wissenschaften zu G¨ottingen. Mathematisch-Physikalische Klasse 1926: 8–22.Suche in Google Scholar

[11] CHEBAN, D.: Asymptotically Almost Periodic Solutions of Almost Periodic Solutions for Some Linear Forced Differential Equations, Hindawi Publishing Corporation, New York, N. Y., 2009.10.1155/9789774540998Suche in Google Scholar

[12] CIEUTAT, P. — HARAUX, A.: Exponential decay and existence of almost periodic solutions for some linear forced differential equations, Port. Math. 59(2) 2002, 141–159.Suche in Google Scholar

[13] COPPEL, W. A.: Almost periodic properties of ordinary differential equations, Ann. Mat. Pura Appl. 76(1) (1967), 27–49.10.1007/BF02412227Suche in Google Scholar

[14] CORDUNEAU, C.: Almost Periodic Functions, Second English Edition, Chelsea Publishing company, New York, N.Y, 1989.Suche in Google Scholar

[15] FAVARD, J.: Sur les ´equations diff´erentielles `a coefficients presque-p´eriodiques, Acta Math. 51 (1927), 31–81 (in French).10.1007/BF02545660Suche in Google Scholar

[16] FINK, A. M.: Almost Periodic Differential Equations. Lecture Notes in Mathematics, Vol. 377, Springer-Verlag, 1974.10.1007/BFb0070324Suche in Google Scholar

[17] GRIFONE, J.: Alg`ebre lin´eaire, Cepadues ´Editions, Toulouse, 1990.Suche in Google Scholar

[18] LANG, S.: Alg`ebre Lin´eaire 1, French Edition, InterEditions, Paris, 1976.Suche in Google Scholar

[19] LEVITAN, M.: Almost Periodic Functions, G.I.T T.L., Moscow, 1959, (in Russian).Suche in Google Scholar

[20] LEVITAN, B. M. — ZHIKOV, V. V.: Almost Periodic Functions and Differential Equations, Cambridge University Press, Cambrigde, New York, 1982.Suche in Google Scholar

[21] LIN, Z. — LIN, Y. X.: Linear Systems, Exponential Dichotomy, and Structure of Sets of Hyperbolic Points, World Scientific, Singapore, 2000.10.1142/4400Suche in Google Scholar

[22] MUHAMADIEV, E.: The invertibility of differential operators in the space of functions that are continuous and bounded on the real axis, Dokl. Akad. Nauk SSSR 196(1), (1971), 47–49, (in Russian).Suche in Google Scholar

[23] ORTEGA, R. — TARALLO, M.: Almost periodic linear differential equations with non separated solutions, J. Funct. Anal. 237 (2006), 402–426.10.1016/j.jfa.2006.03.027Suche in Google Scholar

[24] PANKOV, A.: Bounded and Almost Periodic Solutions of Nonlinear Operator Differential Equations, Kluwer Acad. Publ., Dordrecht, 1990.10.1007/978-94-011-9682-6Suche in Google Scholar

[25] PIAO, D.: Periodic and almost periodic solutions for differential equations with reflection of the argument, Nonlinear Anal. 57 (2004), 633–637.10.1016/j.na.2004.03.017Suche in Google Scholar

[26] PIAO, D.: Pseudo almost periodic solutions for differential equations involving reflection of the argument, J. Korean Math. Soc. 4(41) (2004), 747–754.10.4134/JKMS.2004.41.4.747Suche in Google Scholar

[27] PIAO, D. — SUN, J.: Besicovitch almost periodic solutions for a class of second order differential equations involving reflection of the argument, Electron. J. Qual. Theory Differ. Equ. 41 (2014), 1–8.10.14232/ejqtde.2014.1.41Suche in Google Scholar

[28] PROUSE, G.: Almost-Periodic Functions and Functional Analysis, von Nostrand Reinhold Co., New York, 1971.10.1007/978-1-4757-1254-4Suche in Google Scholar

[29] SEIFERT, G.: Almost periodic solutions for almost periodic systems of ordinary differential equations, J. Differential Equations 2 (1966), 305–319.10.1016/0022-0396(66)90071-4Suche in Google Scholar

[30] TARALLO, M.: Fredholm alternative for a class of almost periodic linear systems, Discrete Contin. Dyn. Syst. 32(6) (2012), 2301–2313.10.3934/dcds.2012.32.2301Suche in Google Scholar

[31] YOSHIZAWA, T.: Stability Theory and the Existence of Periodic Solutions and Almost Periodic Solutions, Springer, New-york, 1975.10.1007/978-1-4612-6376-0Suche in Google Scholar

[32] ZAIDMAN, S.: Almost-Periodic Functions in Abstract Spaces. Research Notes in Mathematics, vol. 126, Pitman, Boston, Mass, USA, 1985.Suche in Google Scholar