Journal of Applied Mathematics
Volume 2012 (2012), Article ID 463913, 19 pages
Research Article

Almost Periodic Solutions to Dynamic Equations on Time Scales and Applications

Department of Mathematics, Yunnan University, Yunnan, Kunming 650091, China

Received 13 January 2012; Accepted 19 August 2012

Academic Editor: Shiping Lu

Copyright © 2012 Yongkun Li and Chao Wang. 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 first introduce the concept of admitting an exponential dichotomy to a class of linear dynamic equations on time scales and study the existence and uniqueness of almost periodic solution and its expression form to this class of linear dynamic equations on time scales. Then, as an application, using these concepts and results, we establish sufficient conditions for the existence and exponential stability of almost periodic solution to a class of Hopfield neural networks with delays. Finally, two examples and numerical simulations given to illustrate our results are plausible and meaningful.