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

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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.

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Correspondence to Q-Heung Choi.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Jung, T., Choi, Q. An Application of Category Theory to a Class of the Systems of the Superquadratic Wave Equations. J Inequal Appl 2010, 850602 (2010) doi:10.1155/2010/850602

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Keywords

  • Boundary Condition
  • Wave Equation
  • Variational Method
  • Dirichlet Boundary
  • Nonlinear Term