×

Periodic and asymptotically periodic solutions of systems of nonlinear difference equations with infinite delay. (English) Zbl 1278.39020

Summary: In this paper we study the existence of periodic and asymptotically periodic solutions of a system of nonlinear Volterra difference equations with infinite delay. By means of fixed point theory, we furnish conditions that guarantee the existence of such periodic solutions.

MSC:

39A23 Periodic solutions of difference equations
39A24 Almost periodic solutions of difference equations
34A34 Nonlinear ordinary differential equations and systems
34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] Agarwal R.P., Monographs and Textbooks in Pure and Applied Mathematics, 2. ed. (2000)
[2] Appleby J.D., Int. J. Difference Equ. 4 (2) pp 165– (2009)
[3] DOI: 10.1017/CBO9780511569975.002 · doi:10.1017/CBO9780511569975.002
[4] Burton T.A., Fixed Point Theory 9 (1) pp 47– (2008)
[5] DOI: 10.1080/10236190008808222 · Zbl 0953.39007 · doi:10.1080/10236190008808222
[6] DOI: 10.1080/10236190802653653 · Zbl 1180.39022 · doi:10.1080/10236190802653653
[7] DOI: 10.1016/j.camwa.2010.01.055 · Zbl 1202.39013 · doi:10.1016/j.camwa.2010.01.055
[8] DOI: 10.1006/jmaa.1994.1037 · Zbl 0796.39004 · doi:10.1006/jmaa.1994.1037
[9] DOI: 10.1080/10236199908808167 · Zbl 0923.39004 · doi:10.1080/10236199908808167
[10] DOI: 10.1080/1023619021000035836 · Zbl 1033.39009 · doi:10.1080/1023619021000035836
[11] Periodic solutions in coupled nonlinear systems of Volterra integro-differential equations
[12] DOI: 10.1080/1023619021000000942 · Zbl 1023.34045 · doi:10.1080/1023619021000000942
[13] DOI: 10.1016/S0362-546X(03)00021-X · Zbl 1031.39005 · doi:10.1016/S0362-546X(03)00021-X
[14] DOI: 10.1016/S0096-3003(03)00791-4 · Zbl 1059.39005 · doi:10.1016/S0096-3003(03)00791-4
[15] Liao X.Y., Nonlinear Stud. 14 (4) pp 311– (2007)
[16] Medina R., Comput. Math. Appl. 181 (1) pp 19– (1994)
[17] DOI: 10.1016/S0898-1221(00)00312-6 · Zbl 0985.39013 · doi:10.1016/S0898-1221(00)00312-6
[18] DOI: 10.1137/040607058 · Zbl 1104.65133 · doi:10.1137/040607058
[19] DOI: 10.1007/s11072-006-0023-4 · Zbl 1262.39008 · doi:10.1007/s11072-006-0023-4
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.