Existence of Positive Solutions for Nonlinear Noncoercive Hemivariational Inequalities

Canadian mathematical bulletin

关键词: $p$-Laplacian;    locally Lipschitz potential;    nonsmooth critical point theory;    principal eigenvalue;    positive solutions;    nonsmooth Mountain Pass Theorem;   

DOI  :  10.4153/CMB-2007-034-6

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

In this paper we investigate the existence of positive solutionsfor nonlinear elliptic problems driven by the $p$-Laplacian with anonsmooth potential (hemivariational inequality). Under asymptoticconditions that make the Euler functional indefinite andincorporate in our framework the asymptotically linear problems,using a variational approach based on nonsmooth critical pointtheory, we obtain positive smooth solutions. Our analysis alsoleads naturally to multiplicity results.

【 授权许可】

Unknown