Periodic Solutions for Neutral Nonlinear Difference Equations with Functional Delay

Imene Soualhia, Abdelouaheb Ardjouni, Ahcene Djoudi

We use a variant of Krasnoselskii's fixed point theorem to show that the nonlinear difference equation with functional delay $\Delta x(t) = -a(t) g(x(t)) + c(t)\Delta x(t -\tau(t)) + q(t, x(t), x(t-\tau(t)))$, 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.