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

• Main Authors: You-Hui Su, Wan-Tong Li
• Format: Article
• Language: English
• Published: Hindawi Limited 2009-01-01
• Series: Discrete Dynamics in Nature and Society
• Online Access: http://dx.doi.org/10.1155/2009/328479

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.