Boundary Value Problems
Volume 2008 (2008), Article ID 293987, 17 pages
Research Article

Existence of Four Solutions of Some Nonlinear Hamiltonian System

Tacksun Jung1 and Q-Heung Choi2

1Department of Mathematics, Kunsan National University, Kunsan 573-701, South Korea
2Department of Mathematics Education, Inha University, Incheon 402-751, South Korea

Received 25 August 2007; Accepted 3 December 2007

Academic Editor: Kanishka Perera

Copyright © 2008 Tacksun Jung and Q-Heung Choi. 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.


We show the existence of four 2π-periodic solutions of the nonlinear Hamiltonian system with some conditions. We prove this problem by investigating the geometry of the sublevels of the functional and two pairs of sphere-torus variational linking inequalities of the functional and applying the critical point theory induced from the limit relative category.