EXISTENCE OF POSITIVE PERIODIC SOLUTIONS FOR A NONLINEAR NEUTRAL DIFFERENCE EQUATION WITH VARIABLE DELAY

ABDELOUAHEB  ARDJOUNI; AHCENE  DJOUDI

EXISTENCE OF POSITIVE PERIODIC SOLUTIONS FOR A NONLINEAR NEUTRAL DIFFERENCE EQUATION WITH VARIABLE DELAY

Authors

ABDELOUAHEB ARDJOUNI Department of Mathematics, Faculty of Sciences,University of Annaba, P.O. Box 12 Annaba, Algeria
AHCENE DJOUDI Department of Mathematics, Faculty of Sciences,University of Annaba, P.O. Box 12 Annaba, Algeria

Keywords:

Positive periodic solutions, nonlinear neutral difference equations, fixed point theorem

Abstract

In this paper, we study the existence of positive periodic solutions of the nonlinear neutral difference equation 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. The results obtained here generalize the work of Raffoul and Yankson [7].