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Periodic solutions in nonlinear neutral differential equations with functional delay. (English) Zbl 1070.39020

The authors consider the nonlinear neutral difference equation \[ x(t+1)=a(t)x(t) + c(t)\Delta x(t-g(t))+q(t,x(t),x(t-g(t)),\tag{1} \] where \(t\in\mathbb{Z}\), \(\Delta x(n) = x(n+1)-x(n)\), right-hand side of (1) is periodic in \(t.\) Using the Krasnoselskii fixed point theorem, conditions for the existence of periodic solutions of (1) are obtained. Applying the contraction mapping principle, the uniqueness of the periodic solution is shown.

MSC:

39A11 Stability of difference equations (MSC2000)
39A12 Discrete version of topics in analysis
34C25 Periodic solutions to ordinary differential equations
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