Nonsmooth critical point theory and nonlinear elliptic equations at resonance

Journal of the Australian Mathematical Society

Nikolaos C. Kourogenis¹ 

[1] Nikolaos S. Papageorgiou

关键词: primary 35J20;    35R70;    49F15;    58E05;   

DOI  :  10.1017/S1446788700002202

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

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 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