PERIODIC SOLUTIONS IN NONLINEAR NEUTRAL DIFFERENCE EQUATIONS WITH FUNCTIONAL DELAY

- Journal title : Journal of the Korean Mathematical Society
- Volume 42, Issue 2, 2005, pp.255-268
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/JKMS.2005.42.2.255

Title & Authors

PERIODIC SOLUTIONS IN NONLINEAR NEUTRAL DIFFERENCE EQUATIONS WITH FUNCTIONAL DELAY

MAROUN MARIETTE R.; RAFFOUL YOUSSEF N.;

MAROUN MARIETTE R.; RAFFOUL YOUSSEF N.;

Abstract

We use Krasnoselskii's fixed point theorem to show that the nonlinear neutral difference equation with delay x(t + 1) = a(t)x(t) + c(t)x(t - g(t)) + q(t, x(t), x(t - g(t)) has a periodic solution. To apply Krasnoselskii's fixed point theorem, one would need to construct two mappings; one is contraction and the other is compact. Also, by making use of the variation of parameters techniques we are able, using the contraction mapping principle, to show that the periodic solution is unique.

Keywords

Krasnoselski;contraction;nonlinear neutral difference equation;periodic solutions;unique solution;

Language

English

Cited by

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