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Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 784198, 11 pages
http://dx.doi.org/10.1155/2013/784198
Research Article

Almost Periodic Solutions for Second Order Dynamic Equations on Time Scales

1School of Mathematical Sciences, Dalian University of Technology, Dalian, Liaoning 116024, China
2College of Mathematics and Computational Science, Shenzhen University, Shenzhen 518060, China

Received 25 July 2013; Accepted 3 September 2013

Academic Editor: Mustafa R. S. Kulenovic

Copyright © 2013 Yan Wang and Lan Li. 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 firstly introduce the concept and the properties of almost periodic functions on time scales, which generalizes the concept of almost periodic functions on time scales and the concept of -almost periodic functions. Secondly, we consider the existence and uniqueness of almost periodic solutions for second order dynamic equations on time scales by Schauder’s fixed point theorem and contracting mapping principle. At last, we obtain alternative theorems for second order dynamic equations on time scales.