Existence of positive solutions for nth-order periodic difference equations

Abstract

This paper is devoted to the study of difference equations coupled with periodic boundary value conditions. We deduce the existence of at least one positive solution provided that the nonlinear part of the equation satis_es some monotonicity assumptions and the existence of a positive upper solution. The result is obtained from a new _xed point theorem based on the classical Krasnoselskii's cone expansion/contraction theorem and the constant sign properties of the related Green's function.