Journal of Inequalities and Applications
Volume 2009 (2009), Article ID 369185, 11 pages
doi:10.1155/2009/369185
Research Article

Integrodifferential Inequality for Stability of Singularly Perturbed Impulsive Delay Integrodifferential Equations

Danhua He1 and Liguang Xu2

1Yangtze Center of Mathematics, Sichuan University, Chengdu 610064, China
2Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou 310023, China

Received 24 February 2009; Accepted 11 June 2009

Academic Editor: Ondrej Dosly

Copyright © 2009 Danhua He and Liguang Xu. 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 exponential stability of singularly perturbed impulsive delay integrodifferential equations (SPIDIDEs) is concerned. By establishing an impulsive delay integrodifferential inequality (IDIDI), some sufficient conditions ensuring the exponentially stable of any solution of SPIDIDEs for sufficiently small ε>0 are obtained. A numerical example shows the effectiveness of our theoretical results.