Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 850602, 16 pages
doi:10.1155/2010/850602
Research Article

An Application of Category Theory to a Class of the Systems of the Superquadratic Wave Equations

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 16 October 2009; Accepted 7 February 2010

Academic Editor: Jong Kkyungnam Kim

Copyright © 2010 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.

Abstract

We investigate the nontrivial solutions for a class of the systems of the superquadratic nonlinear wave equations with Dirichlet boundary condition and periodic condition with a superquadratic nonlinear terms at infinity which have continuous derivatives. We approach the variational method and use the critical point theory on the manifold, in terms of the limit relative category of the sublevel subsets of the corresponding functional.