Nontrivial Solutions of a Nonlinear Wave Equation with Jumping Nonlinearity

Hunan Xu; Q-Heung Choi

Title	Nontrivial Solutions of a Nonlinear Wave Equation with Jumping Nonlinearity
Publication Type	Journal Article
Year of Publication	2005
Authors	Xu, H, Choi, Q-H
Volume	9
Issue	4
Start Page	465
Pagination	16
Date Published	2005
ISSN	1083-2564
AMS	35B10, 35B38, 35L05
Abstract	In this paper we study the multiplicity of nontrivial solutions for nonlinear wave equation of the form${ u_{tt} − u_{xx} = b[(u + 1)^+ − 1] }$ in ${ (c, d) × \mathbb{R} }$ with Dirichlet boundary condition on the interval ${ c < x < d }$. We find the multiple nontrivial solutions of the equation. Here we reduce this problem into a two-dimensional problem by using variational reduction method and apply the Mountain Pass theorem to find the nontrivial solutions
URL	http://www.acadsol.eu/en/articles/9/4/3.pdf
Refereed Designation	Refereed
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