Electron. J. Diff. Eqns., Vol. 2006(2006), No. 134, pp. 1-12.

Periodic solutions for second-order Hamiltonian systems with the p-Laplacian

Yu Tian, Weigao Ge

In this paper, we investigate the periodic solutions of Hamiltonian system with the p-Laplacian. By using Mountain Pass Theorem the existence of at least one periodic solution is obtained, Furthermore, under suitable assumptions, we obtain the existence of infinitely many solutions via $Z_2$-symmetric version of the Mountain Pass Theorem.

Submitted July 16, 2006. Published October 19, 2006.
Math Subject Classifications: 34B15, 58E30.
Key Words: Hamiltonian system; p-Laplacian; Mountain Pass Theorem; Periodic solution.

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Yu Tian
School of Science
Beijing University of Posts and Telecommunications
Beijing 100876, China
email: tianyu2992@163.com
  Weigao Ge
Department of Applied Mathematics
Beijing Institute of Technology, Beijing 100081, China
email: gew@bit.edu.cn

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