Periodic solutions for neutral nonlinear difference equations with functional delay

Abstract

We use a variant of Krasnoselskii's fixed point theorem to show that the nonlinear difference equation with functional delay Δx (t) = - a (t) g (x (t)) + c (t)Δx(t_τ(t)) + q (t, x(t), x(t_τ(t))), has periodic solutions. For that end, we invert this equation to construct a fixed point mapping written as a sum of a completely continuous map and a large contraction which is suitable for the application of Krasnoselskii-Burton's theorem.

Keywords

• krasnoselskii theorem
• fixed point
• periodic solutions
• large contraction
• difference equations