Boundary Value Problems 
Volume 2008 (2008), Article ID 293987, 17 pages
doi:10.1155/2008/293987
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

Recommended by Kanishka Perera

Abstract

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.