On positive periodic solutions of linear second order functional differential equations

References

[1] Azbelev N. V., Maksimov V. P. and Rakhmatullina L. F., Introduction to the Theory of Functional Differential Equations: Methods and Applications, Contemp. Math. Appl. 3, Hindawi Publishing, Cairo, 2007. 10.1155/9789775945495Search in Google Scholar

[2] Bravyi E. I., Solvability of the periodic problem for higher-order linear functional differential equations (in Russian), Differ. Uravn. 51 (2015), no. 5, 563–577; translation in Differ. Equ. 51 (2015), no. 5, 571–585. 10.1134/S0012266115050018Search in Google Scholar

[3] Bravyi E. I., On solvability of periodic boundary value problems for second order linear functional differential equations, Electron. J. Qual. Theory Differ. Equ. 2016 (2016), Paper No. 5. 10.14232/ejqtde.2016.1.5Search in Google Scholar

[4] Domoshnitsky A., Hakl R. and Šremr J., Component-wise positivity of solutions to periodic boundary problem for linear functional differential system, J. Inequal. Appl. 2012 (2012), Article ID 112. 10.1186/1029-242X-2012-112Search in Google Scholar

[5] Fu X. and Wang W., Periodic boundary value problems for second-order functional differential equations, J. Inequal. Appl. 2010 (2010), Article ID 598405. 10.1155/2010/598405Search in Google Scholar

[6] Hakl R. and Mukhigulashvili S., A periodic boundary value problem for functional differential equations of higher order, Georgian Math. J. 16 (2009), no. 4, 651–665. 10.1515/GMJ.2009.651Search in Google Scholar

[7] Hou X. and Wu Z., Existence and uniqueness of periodic solutions for a kind of Liénard equation with multiple deviating arguments, J. Appl. Math. Comput. 38 (2012), no. 1–2, 181–193. 10.1007/s12190-010-0472-xSearch in Google Scholar

[8] Jiang D., Nieto J. J. and Zuo W., On monotone method for first and second order periodic boundary value problems and periodic solutions of functional differential equations, J. Math. Anal. Appl. 289 (2004), no. 2, 691–699. 10.1016/j.jmaa.2003.09.020Search in Google Scholar

[9] Kiguradze I., Partsvania N. and Půža B., On periodic solutions of higher-order functional differential equations, Bound. Value Probl. 2008 (2008), Article ID 389028. 10.1155/2008/389028Search in Google Scholar

[10] Kiguradze I. and Sokhadze Z., Positive solutions of periodic type boundary value problems for first order singular functional differential equations, Georgian Math. J. 21 (2014), no. 3, 303–311. 10.1515/gmj-2014-0030Search in Google Scholar

[11] Li J., Luo J. and Cai Y., Periodic solutions for prescribed mean curvature Rayleigh equation with a deviating argument, Adv. Difference Equ. 2013 (2013), 10.1186/1687-1847-2013-88. 10.1186/1687-1847-2013-88Search in Google Scholar

[12] Li Q. and Li Y., Existence and multiplicity of positive periodic solutions for second-order functional differential equations with infinite delay, Electron. J. Differential Equations 2014 (2014), Paper No. 93. Search in Google Scholar

[13] Lomtatidze A. and Mukhigulashvili S., On periodic solutions of second order functional differential equations, Mem. Differ. Equ. Math. Phys. 5 (1995), 125–126. Search in Google Scholar

[14] Lomtatidze A., Půža B. and Hakl R., On a periodic boundary value problem for first-order functional-differential equations (in Russian), Differ. Uravn. 39 (2003), no. 3, 320–327; translation in Differ. Equ. 39 (2003), no. 3, 344–352. Search in Google Scholar

[15] Lu S. and Ge W., Sufficient conditions for the existence of periodic solutions to some second order differential equations with a deviating argument, J. Math. Anal. Appl. 308 (2005), no. 2, 393–419. 10.1016/j.jmaa.2004.09.010Search in Google Scholar

[16] Ma R. and Lu Y., Existence of positive periodic solutions for second-order functional differential equations, Monatsh. Math. 173 (2014), no. 1, 67–81. 10.1007/s00605-012-0471-0Search in Google Scholar

[17] Mukhigulashvili S. V., On the unique solvability of the Dirichlet problem for a second-order linear functional-differential equation (in Russian), Differ. Uravn. 40 (2004), no. 4, 477–484; translation in Differ. Equ. 40 (2004), no. 4, 515–523. 10.1023/B:DIEQ.0000035789.25629.86Search in Google Scholar

[18] Mukhigulashvili S., On a periodic boundary value problem for third order linear functional differential equations, Nonlinear Anal. 66 (2007), no. 2, 527–535. 10.1016/j.na.2005.11.046Search in Google Scholar

[19] Mukhigulashvili S., Partsvania N. and Půža B., On a periodic problem for higher-order differential equations with a deviating argument, Nonlinear Anal. 74 (2011), no. 10, 3232–3241. 10.1016/j.na.2011.02.002Search in Google Scholar

[20] Ren J., Cheung W. and Cheng Z., Existence and Lyapunov stability of periodic solutions for generalized higher-order neutral differential equations, Bound. Value Probl. 2011 (2011), Article ID 635767. 10.1155/2011/635767Search in Google Scholar

[21] Saker S. H. and Agarwal S., Oscillation and global attractivity in a nonlinear delay periodic model of respiratory dynamics, Comput. Math. Appl. 44 (2002), no. 5–6, 623–632. 10.1016/S0898-1221(02)00177-3Search in Google Scholar

[22] Song B., Pan L. and Cao J., Periodic solutions for a class of n-th order functional differential equations, Int. J. Differ. Equ. 2011 (2011), Article ID 916279. 10.1155/2011/916279Search in Google Scholar

[23] Wang H., Positive periodic solutions of functional differential equations, J. Differential Equations 202 (2004), no. 2, 354–366. 10.1016/j.jde.2004.02.018Search in Google Scholar

[24] Wang W., Shen J. and Nieto J. J., Periodic boundary value problems for second order functional differential equations, J. Appl. Math. Comput. 36 (2011), no. 1–2, 173–186. 10.1007/s12190-010-0395-6Search in Google Scholar

[25] Wu Y., Existence of positive periodic solutions for a functional differential equation with a parameter, Nonlinear Anal. 68 (2008), no. 7, 1954–1962. 10.1016/j.na.2007.01.022Search in Google Scholar

[26] Wu Y., Existence nonexistence and multiplicity of periodic solutions for a kind of functional differential equation with parameter, Nonlinear Anal. 70 (2009), no. 1, 433–443. 10.1016/j.na.2007.12.011Search in Google Scholar