Abstract
We obtain sufficient conditions for the existence and uniqueness of continuous N-periodic solutions (N is a positive integer number) for a certain class of systems of nonlinear difference equations with continuous argument and study their properties.
Similar content being viewed by others
References
G. D. Birkhoff, “General theory of linear difference equations,” Trans. Amer. Math. Soc., 12, No. 2, 242–284 (1911).
A. Guldberg and G. Wallenberg, Theorie der linearen Differenzengleichungen, Teubner, Leipzig-Berlin (1911).
Yu. A. Mitropol’skii, D. I. Martynyuk, and A. M. Samoilenko, Systems of Evolution Equations with Periodic and Quasiperiodic Coefficients [in Russian], Naukova Dumka, Kiev (1984).
A. A. Mirolyubov and M. A. Soldatov, Linear Inhomogeneous Difference Equations [in Russian], Nauka, Moscow (1986).
H. P. Pelyukh and N. A. Bohai, “Investigation of the structure of the set of continuous solutions of systems of linear difference equations with continuous argument,” Nelin. Kolyvannya, 8, No. 3, 351–359 (2005).
G. P. Pelyukh, “On the theory of linear difference equations with periodic coefficients,” Dokl. Ros. Akad. Nauk, 336, No. 4, 451–452 (1994).
G. P. Pelyukh, “On the existence of periodic solutions of nonlinear difference equations,” Ukr. Mat. Zh., 54, No. 12, 1626–1633 (2002).
Author information
Authors and Affiliations
Additional information
__________
Translated from Neliniini Kolyvannya, Vol. 10, No. 2, pp. 177–183, April–June, 2007.
Rights and permissions
About this article
Cite this article
Bohai, N.A. Continuous solutions of systems of nonlinear difference equations with continuous argument and their properties. Nonlinear Oscill 10, 169–175 (2007). https://doi.org/10.1007/s11072-007-0013-1
Received:
Issue Date:
DOI: https://doi.org/10.1007/s11072-007-0013-1