Existence of four solutions for the elliptic problem with nonlinearity crossing one eigenvalue

Journal of inequalities and applications

Tacksun Jung¹ 

关键词: elliptic boundary value problem;    jumping nonlinearity;    inverse compact operator;    variational reduction method;    Leray-Schauder degree theory;   

DOI  :  10.1186/1029-242X-2013-187

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

We investigate the multiplicity of the weak solutions for the nonlinear elliptic boundary value problem. We get a theorem which shows the existence of at least four weak solutions for the asymptotically linear elliptic problem with Dirichlet boundary condition. We obtain this result by using the Leray-Schauder degree theory, the variational reduction method and critical point theory. MSC:35J15, 35J25.

【 授权许可】

CC BY