DCDS
A nonlinear wave equation with jumping nonlinearity
Q-Heung Choi Tacksun Jung
Discrete & Continuous Dynamical Systems - A 2000, 6(4): 797-802 doi: 10.3934/dcds.2000.6.797
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 $\phi_{0 0}$, $\phi_{10}$.
keywords: eigenfunction. eigenvalue Multiplicity of solutions
CPAA
The multiplicity of solutions and geometry in a wave equation
Q-Heung Choi Changbum Chun Tacksun Jung
Communications on Pure & Applied Analysis 2003, 2(2): 159-170 doi: 10.3934/cpaa.2003.2.159
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 Dirichlet boundary condition. eigenfunction eigenvalue

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