Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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SIGN CHANGING PERIODIC SOLUTIONS OF A NONLINEAR WAVE EQUATION

  • Jung, Tacksun (Department of Mathematics Kunsan National University) ;
  • Choi, Q-Heung (Department of Mathematics Education Inha University)
  • Received : 2008.06.03
  • Published : 2008.06.10
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Abstract

We seek the sign changing periodic solutions of the nonlinear wave equation $u_{tt}-u_{xx}=a(x,t)g(u)$ under Dirichlet boundary and periodic conditions. We show that the problem has at least one solution or two solutions whether $\frac{1}{2}g(u)u-G(u)$ is bounded or not.

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