Advances in Difference Equations
Volume 2007 (2007), Article ID 35378, 21 pages
doi:10.1155/2007/35378
Research Article

Variationally Asymptotically Stable Difference Systems

Sung Kyu Choi,1 Yoon Hoe Goo,2 and Namjip Koo1

1Department of Mathematics, Chungnam National University, Daejeon 305-764, Korea
2Department of Mathematics, Hanseo University, Seosan, Chungnam 352-820, Korea

Received 3 January 2007; Revised 10 May 2007; Accepted 9 August 2007

Academic Editor: Leonid E. Shaikhet

Copyright © 2007 Sung Kyu Choi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We characterize the h-stability in variation and asymptotic equilibrium in variation for nonlinear difference systems via n∞-summable similarity and comparison principle. Furthermore we study the asymptotic equivalence between nonlinear difference systems and their variational difference systems by means of asymptotic equilibria of two systems.