Multiplicity of Nontrivial Solutions for Elliptic Equations with Nonsmooth Potential and Resonance at Higher Eigenvalues

Proceedings Mathematical Sciences

Dumitru Motreanu¹  Nikolaos S Papageorgiou²  Leszek GasiÅ„ski³ 

[1] Département de Mathematiques, Université de Perpignan, 0 Perpignan, France$$;Department of Mathematics, National Technical University, Zografou Campus, Athens 0, Greece$$;Institute of Computer Science, Jagiellonian University, ul. Nawojki , 00 Cracow, Poland$$

关键词: Double resonance;    reduction method;    eigenvalue;    hemivariational inequality;    locally Lipschitz function;    Clarke subdifferential;    critical point;    local linking;    nonsmooth Cerami condition.;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

We consider a semilinear elliptic equation with a nonsmooth, locally Lipschitz potential function (hemivariational inequality). Our hypotheses permit double resonance at infinity and at zero (double-double resonance situation). Our approach is based on the nonsmooth critical point theory for locally Lipschitz functionals and uses an abstract multiplicity result under local linking and an extension of the Castro–Lazer–Thews reduction method to a nonsmooth setting, which we develop here using tools from nonsmooth analysis.

【 授权许可】

Unknown