October  2000, 6(4): 797-802. doi: 10.3934/dcds.2000.6.797

A nonlinear wave equation with jumping nonlinearity

1. 

Department of Mathematics, Inha University, Incheon 402-751

2. 

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

Received  August 1999 Revised  May 2000 Published  August 2000

We investigate multiplicity of solutions $u(x,t)$ for a piecewise linear perturbation of the one-dimensional wave operator $u_{t t} - u_{x x}$ under Dirichlet boundary condition on the interval $(-\pi/2, \pi/2)$ and periodic condition on the variable $t$. Our concern is to investigate a relation between multiplicity of solutions and source terms of (1.4) when the nonlinearity $-(bu^+ -au^-)$ crosses two eigenvalues and the source term $f$ is generated by two eigenfunctions $\phi_{0 0}$, $\phi_{10}$.
Citation: Q-Heung Choi, Tacksun Jung. A nonlinear wave equation with jumping nonlinearity. Discrete & Continuous Dynamical Systems - A, 2000, 6 (4) : 797-802. doi: 10.3934/dcds.2000.6.797
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