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

Yoshihiro Hamaya

doi:10.3934/proc.2009.2009.315

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2009, Volume 2009: 315-321. Doi: 10.3934/proc.2009.2009.315 open access

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

Yoshihiro Hamaya^1,

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

Received: June 30, 2008

Revised: March 31, 2009

Published: August 2009

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Abstract

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:

Volterra difference equations,
Almost periodic solutions and WUA stable.

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

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