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August  2006, 15(3): 939-950. doi: 10.3934/dcds.2006.15.939

Periodic solutions for discrete convex Hamiltonian systems via Clarke duality

Jianshe Yu 1, , Honghua Bin 2, and  Zhiming Guo 3,

1. 

College of Mathematics and Econometrics, Hunan University, College of Mathematics and Information Science, Guangzhou University, Guangzhou, Guangdong, 510405, China
2. 

College of Mathematics and Econometrics, Hunan University, Changsha, Hunan, 410082, China
3. 

College of Mathematics and Information Science, Guangzhou University, Guangzhou, Guangdong, 510405, China

Received  June 2005 Revised  January 2006 Published  April 2006

Based on the Legendre transform, the dual action functional which corresponds to discrete Hamiltonian systems is given. In this paper, the existence of periodic solution for discrete convex Hamiltonian systems with forcing terms is obtained by using the dual least action principle and the perturbation technique.
Keywords: perturbation technique, dual least action principle, discrete Hamiltonian systems, periodic solution, convex., Clarke duality.
Mathematics Subject Classification: 39A1.
Citation: Jianshe Yu, Honghua Bin, Zhiming Guo. Periodic solutions for discrete convex Hamiltonian systems via Clarke duality. Discrete & Continuous Dynamical Systems, 2006, 15 (3) : 939-950. doi: 10.3934/dcds.2006.15.939
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