Periodic Solutions for Neutral Nonlinear Difference Equations with Functional Delay
Mathematica Moravica, Tome 20 (2016) no. 1.

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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.
Mots-clés : Krasnoselskii theorem, Fixed point, Periodic solutions, Large contraction, Difference equations 
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Imene Soualhia; Abdelouaheb Ardjouni; Ahcene Djoudi. Periodic Solutions for Neutral Nonlinear Difference Equations with Functional Delay. Mathematica Moravica, Tome 20 (2016) no. 1. https://geodesic-test.mathdoc.fr/item/MM3_2016_20_1_a2/