Bounded solutions for the nonlinear wave equation

Boundary value problems

Q-Heung Choi¹  Tacksun Jung² 

[1] Department of Mathematics Education, Inha University, Incheon, Korea;Department of Mathematics, Kunsan National University, Kunsan, Korea

关键词: wave equation;    critical point theory;    invariant function;    invariant subspace;    eigenvalue problem;   

DOI  :  10.1186/1687-2770-2013-257

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

We investigate the number of periodic weak solutions for the wave equation with nonlinearity decaying at the origin. We get a theorem which shows the existence of a bounded weak solution for this problem. We obtain this result by approaching the variational method and applying the critical point theory for the indefinite functional induced from the invariant subspaces and the invariant functional. MSC:35L05, 35L70.

【 授权许可】

CC BY