Discrete Dynamics in Nature and Society
Volume 2009 (2009), Article ID 141929, 27 pages
doi:10.1155/2009/141929
Research Article

Multiple Positive Symmetric Solutions to p-Laplacian Dynamic Equations on Time Scales

You-Hui Su1 and Can-Yun Huang2

1School of Mathematics and Physical Sciences, Xuzhou Institute of Technology, Xuzhou, Jiangsu 221008, China
2Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou 730050, China

Received 1 July 2009; Accepted 18 November 2009

Academic Editor: Leonid Shaikhet

Copyright © 2009 You-Hui Su and Can-Yun Huang. 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

This paper makes a study on the existence of positive solution to p-Laplacian dynamic equations on time scales 𝕋. Some new sufficient conditions are obtained for the existence of at least single or twin positive solutions by using Krasnosel'skii's fixed point theorem and new sufficient conditions are also obtained for the existence of at least triple or arbitrary odd number positive solutions by using generalized Avery-Henderson fixed point theorem and Avery-Peterson fixed point theorem. As applications, two examples are given to illustrate the main results and their differences. These results are even new for the special cases of continuous and discrete equations, as well as in the general time-scale setting.