Stability properties and existence of almost periodic solutions of volterra difference equations

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2009, 2009(Special): 315-321. doi: 10.3934/proc.2009.2009.315

Stability properties and existence of almost periodic solutions of volterra difference equations

1.	Department of Information Science, Okayama University of Science, 1-1 Ridai-cho, Okayama 700-0005, Japan

Received July 2008 Revised April 2009 Published September 2009

Abstract
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In order to obtain the existence of periodic and almost periodic solutions of Volterra difference equation: $ x(n+1)=f(n,x(n))+\sum_{s=-\infty}^{n}F(n,s,x(n+s),x(n)) $, we consider certain two stability properties, which are referred to as (K, $ \rho $)-weakly uniformly asymptotically stable and (K, $ \rho $)-uniformly asymptotically stable.

Keywords: Almost periodic solutions and WUA stable, Volterra difference equations.

Mathematics Subject Classification: Primary: 39A11, 39A12.

Citation: Yoshihiro Hamaya. Stability properties and existence of almost periodic solutions of volterra difference equations. Conference Publications, 2009, 2009 (Special) : 315-321. doi: 10.3934/proc.2009.2009.315

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