Discrete Dynamics in Nature and Society
Volume 2009 (2009), Article ID 328479, 17 pages
doi:10.1155/2009/328479
Periodic solution of second-order Hamiltonian systems with a change sign potential on time scales
You-Hui Su1
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
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.