Discrete Dynamics in Nature and Society
Volume 2011 (2011), Article ID 958381, 22 pages
http://dx.doi.org/10.1155/2011/958381
Research Article

Lyapunov Function and Exponential Trichotomy on Time Scales

Ji Zhang

College of Mathematics, Jilin University, Changchun 130012, China

Received 20 February 2011; Revised 7 May 2011; Accepted 6 July 2011

Academic Editor: Jinde Cao

Copyright © 2011 Ji Zhang. 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 study the relation between Lyapunov function and exponential trichotomy for the linear equation 𝑥 Δ = 𝐴 ( 𝑡 ) 𝑥 on time scales. Furthermore, as an application of these results, we give the roughness of exponential trichotomy on time scales.