Discrete Dynamics in Nature and Society
Volume 2009 (2009), Article ID 140369, 16 pages
Research Article

On Dichotomous Behavior of Variational Difference Equations and Applications

Department of Mathematics, Faculty of Mathematics and Computer Science, West University of Timişoara, V. Pârvan Blvd. No. 4, 300223 Timişoara, Romania

Received 1 December 2008; Accepted 18 March 2009

Academic Editor: Guang Zhang

Copyright © 2009 Bogdan Sasu. 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.


We give new and very general characterizations for uniform exponential dichotomy of variational difference equations in terms of the admissibility of pairs of sequence spaces over with respect to an associated control system. We establish in the variational case the connections between the admissibility of certain pairs of sequence spaces over and the admissibility of the corresponding pairs of sequence spaces over . We apply our results to the study of the existence of exponential dichotomy of linear skew-product flows.