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2014 Existence of Periodic Solutions to Nonlinear Difference Equations at Full Resonance
Z. Abernathy, J. Rodriguez
Commun. Math. Anal. 17(1): 47-56 (2014).

Abstract

The purpose of this paper is to search for periodic solutions to a system of nonlinear difference equations of the form \[\Delta x(t) = f(\epsilon,t,x(t)).\] The corresponding linear homogeneous system has an $n$-dimensional kernel, i.e. the system is at full resonance. We provide sufficient conditions for the existence of periodic solutions based on asymptotic properties of the nonlinearity $f$ when $\epsilon=0$. To this end, we employ a projection method using the Lyapunov-Schmidt procedure together with Brouwer's fixed point theorem.

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Z. Abernathy. J. Rodriguez. "Existence of Periodic Solutions to Nonlinear Difference Equations at Full Resonance." Commun. Math. Anal. 17 (1) 47 - 56, 2014.

Information

Published: 2014
First available in Project Euclid: 10 December 2014

zbMATH: 1321.39020
MathSciNet: MR3285878

Subjects:
Primary: 39A10 , 39A12 , 39A23

Keywords: boundary value problems , Brouwer fixed point theorem , difference equations , Lyapunov-Schmidt procedure , projection

Rights: Copyright © 2014 Mathematical Research Publishers

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