#### Abdelouaheb Ardjouni, Ahcene Djoudi, Existence of positive periodic solutions for a system of nonlinear neutral difference equations with variable delay, 2016 (2016), Article ID 20 (19 April 2016)

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Abstract

In this paper, we study the existence of positive periodic solutions of the system of nonlinear neutral difference equations with variable delay $x(n+1)=A(n)x(n)$ $+\triangle g(n,x(n-\tau(n)))$ $+f(n,x(n-\tau(n))) .$ The main tool employed here is the Krasnoselskii’s hybrid fixed point theorem dealing with a sum of two mappings, one is a contraction and the other is completely continuous.