The multiplicity of solutions and geometry in a wave equation

Pages: 159 - 170, Volume 2, Issue 2, June 2003

doi:10.3934/cpaa.2003.2.159       Abstract        Full Text (198.7K)       Related Articles

Q-Heung Choi - Department of Mathematics, Inha University, Incheon 402-751, South Korea (email)
Changbum Chun - School of Liberal Arts & Education, Korea University of Technology and Education, Cheonan 330-708, South Korea (email)
Tacksun Jung - Department of Mathematics, Kunsan National University, Kunsan 573-701, South Korea (email)

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.

Keywords:  Multiplicity of solutions, eigenvalue, eigenfunction, Dirichlet boundary condition.
Mathematics Subject Classification:  35B10, 35L20.

Received: June 2002;      Revised: January 2003;      Published: March 2003.