Abstract and Applied Analysis
Volume 2011 (2011), Article ID 341520, 22 pages
Research Article

Uniformly Almost Periodic Functions and Almost Periodic Solutions to Dynamic Equations on Time Scales

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

Received 29 April 2011; Revised 27 July 2011; Accepted 25 August 2011

Academic Editor: Detlev Buchholz

Copyright © 2011 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.


Firstly, we propose a concept of uniformly almost periodic functions on almost periodic time scales and investigate some basic properties of them. When time scale or , our definition of the uniformly almost periodic functions is equivalent to the classical definitions of uniformly almost periodic functions and the uniformly almost periodic sequences, respectively. Then, based on these, we study the existence and uniqueness of almost periodic solutions and derive some fundamental conditions of admitting an exponential dichotomy to linear dynamic equations. Finally, as an application of our results, we study the existence of almost periodic solutions for an almost periodic nonlinear dynamic equations on time scales.