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

Journal of Inequalities and Applications20102010:850602

Received: 16 October 2009

Accepted: 7 February 2010

Published: 15 March 2010


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.


Boundary ConditionWave EquationVariational MethodDirichlet BoundaryNonlinear Term

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Authors’ Affiliations

Department of Mathematics, Kunsan National University, Kunsan, South Korea
Department of Mathematics Education, Inha University, Incheon, South Korea


© T. Jung and Q.-H. Choi. 2010

This article is published under license to BioMed Central Ltd. 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.