A nonlinear wave equation with jumping nonlinearity

Q-Heung Choi; Tacksun Jung

doi:10.3934/dcds.2000.6.797

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2000, Volume 6, Issue 4: 797-802. Doi: 10.3934/dcds.2000.6.797

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A nonlinear wave equation with jumping nonlinearity

Q-Heung Choi^1, and
Tacksun Jung²

1.
Department of Mathematics, Inha University, Incheon 402-751
2.
Department of Mathematics, Kunsan National University, Kunsan 573-701

Received: July 31, 1999

Revised: April 30, 2000

Published: September 2000

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Abstract

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 $\phi_{0 0}$, $\phi_{10}$.

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Mathematics Subject Classification: 35B10, 35L20.

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