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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 741696, 23 pages
http://dx.doi.org/10.1155/2012/741696
Research Article

Admissibility for Nonuniform Contraction and Dichotomy

Department of Mathematics, College of Science, Hohai University, Nanjing, Jiangsu 210098, China

Received 4 October 2012; Accepted 27 November 2012

Academic Editor: Juntao Sun

Copyright © 2012 Yongxin Jiang and Fang-fang Liao. 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

The relation between the notions of nonuniform asymptotic stability and admissibility is considered. Using appropriate Lyapunov norms, it is showed that if any of their associated spaces, with , is admissible for a given evolution process, then this process is a nonuniform contraction and dichotomy. A collection of admissible Banach spaces for any given nonuniform contraction and dichotomy is provided.