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A nonlinear wave equation with jumping nonlinearity

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  • 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 $\phi_{0 0}$, $\phi_{10}$.
    Mathematics Subject Classification: 35B10, 35L20.


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