Discrete Dynamics in Nature and Society
Volume 2009 (2009), Article ID 328479, 17 pages
doi:10.1155/2009/328479
Research Article

Periodic Solution of Second-Order Hamiltonian Systems with a Change Sign Potential on Time Scales

You-Hui Su1,2 and Wan-Tong Li2

1School of Mathematics and Physical Sciences, Xuzhou Institute of Technology, Xuzhou, Jiangsu 221008, China
2School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, China

Received 26 November 2008; Accepted 4 April 2009

Academic Editor: Yong Zhou

Copyright © 2009 You-Hui Su and Wan-Tong 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

This paper is concerned with the second-order Hamiltonian system on time scales 𝕋 of the form uΔΔ(ρ(t))+μb(t)|u(t)|μ−2u(t)+∇¯H(t,u(t))=0, Δ-a.e. t∈[0,T]𝕋 , u(0)−u(T)=uΔ(ρ(0))−uΔ(ρ(T))=0, where 0,T∈𝕋. By using the minimax methods in critical theory, an existence theorem of periodic solution for the above system is established. As an application, an example is given to illustrate the result. This is probably the first time the existence of periodic solutions for second-order Hamiltonian system on time scales has been studied by critical theory.