Nonsmooth critical point theory and nonlinear elliptic equations at resonance

Kodai Mathematical Journal

Nikolaos S. Papageorgiou¹  Nikolaos C. Kourogenis¹ 

关键词: Nonsmooth critical point theory;    locally Lipschitz function;    subdifferential;    linking;    nonsmooth Palais-Smale condition;    nonsmooth Cerami condition;    Mountain pass theorem;    Saddle point theorem;    problems at resonance;    p-Laplacian;    first eigenvalue;   

DOI  :  10.2996/kmj/1138044160

学科分类：数学（综合）

来源: Tokyo Institute of Technology, Department of Mathematics

【 摘 要 】

References(26)In this paper we complete two tasks. First we extend the nonsmooth critical point theory of Chang to the case where the energy functional satisfies only the weaker nonsmooth Cerami condition and we also relax the boundary conditions. Then we study semilinear and quasilinear equations (involving the p-Laplacian). Using a variational approach we establish the existence of one and of multiple solutions. In the simple existence theorems, we allow the right hand side to be discontinuous. In that case in order to have an existence theory, we pass to a multivalued approximation of the original problem by, roughly speaking, filling in the gaps at the discontinuity points.

【 授权许可】

Unknown