#### Abdelouaheb Ardjouni, Ahcene Djoudi, Existence of positive periodic solutions of neutral difference equations with variable coefficients, Vol. 2018 (2018), Article ID 19, pp. 1-9

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DOI: 10.23952/cot.2018.19

Received March 29, 2018; Accepted July 17, 2018; Published August 15, 2018

Abstract. In this paper, we study the existence of positive periodic solutions of the nonlinear neutral difference equation with variable coefficients $x(n+1) = a(n) x(n) +\Delta(c(n) x(n-\tau)) + f(n,x(n-\tau))$. The main tool in this paper is the Krasnoselskii’s hybrid fixed point theorem which deals with a sum of two mappings, one is a contraction and the other is completely continuous.