June  2003, 2(2): 159-170. doi: 10.3934/cpaa.2003.2.159

The multiplicity of solutions and geometry in a wave equation

1. 

Department of Mathematics, Inha University, Incheon 402-751, South Korea

2. 

School of Liberal Arts & Education, Korea University of Technology and Education, Cheonan 330-708, South Korea

3. 

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

Received  June 2002 Revised  January 2003 Published  March 2003

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.
Citation: Q-Heung Choi, Changbum Chun, Tacksun Jung. The multiplicity of solutions and geometry in a wave equation. Communications on Pure & Applied Analysis, 2003, 2 (2) : 159-170. doi: 10.3934/cpaa.2003.2.159
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