PERIODIC SOLUTIONS IN NONLINEAR NEUTRAL DIFFERENCE EQUATIONS WITH FUNCTIONAL DELAY

Title & Authors
PERIODIC SOLUTIONS IN NONLINEAR NEUTRAL DIFFERENCE EQUATIONS WITH FUNCTIONAL DELAY
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)$\small{{\Delta}}$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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대한수학회논문집, 2014. vol.29. 1, pp.195-204
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