The multiplicity of solutions and geometry in a wave equation

Q-Heung Choi; Changbum Chun; Tacksun Jung

doi:10.3934/cpaa.2003.2.159

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2003, Volume 2, Issue 2: 159-170. Doi: 10.3934/cpaa.2003.2.159

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The multiplicity of solutions and geometry in a wave equation

1.
Department of Mathematics, Inha University, Incheon 402-751
2.
School of Liberal Arts & Education, Korea University of Technology and Education, Cheonan 330-708
3.
Department of Mathematics, Kunsan National University, Kunsan 573-701

Received: May 31, 2002

Revised: December 31, 2002

Published: May 2003

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Abstract

We investigate multiplicity of solutions of the nonlinear one dimensional wave equation with Dirichlet boundary condition on the interval $(-\frac{\pi}{2},\frac{\pi}{2})$ and periodic condition on the variable $t.$ Our concern is to investigate a relation between multiplicity of solutions and source terms of the equation when the nonlinearity $-(bu^{+} - a u^{-})$ crosses an eigenvalue $\lambda_{10}$ and the source term $f$ is generated by three eigenfunctions.

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Mathematics Subject Classification: 35B10, 35L20.

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