Open Access Research

Weak solutions for the singular potential wave system

Tacksun Jung1 and Q-Heung Choi2*

Author Affiliations

1 Department of Mathematics, Kunsan National University, Kunsan, 573-701, Korea

2 Department of Mathematics Education, Inha University, Incheon, 402-751, Korea

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Boundary Value Problems 2014, 2014:7  doi:10.1186/1687-2770-2014-7

Published: 7 January 2014

Abstract

We investigate the existence of weak solutions for a class of the system of wave equations with singular potential nonlinearity. We obtain a theorem which shows the existence of nontrivial weak solution for a class of the wave system with singular potential nonlinearity and the Dirichlet boundary condition. We obtain this result by using the variational method and critical point theory for indefinite functional.

MSC: 35L51, 35L70.

Keywords:
class of wave system; singular potential nonlinearity; Dirichlet boundary condition; variational method; critical point theorem for indefinite functional; <a onClick="popup('http://www.boundaryvalueproblems.com/content/2014/1/7/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2014/1/7/mathml/M1">View MathML</a> condition