Superlinear elliptic hemivariational inequalities

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Hacettepe Journal of Mathematics and Statistics
Volume:52 Issue:6 - Special Issue:Nonlinear Evolution Problems with Applications
Superlinear elliptic hemivariational inequalities

Superlinear elliptic hemivariational inequalities

Authors : Yunru Bai, Leszek Gasinski, Nikolaos Papageorgiou

Pages : 1631-1657

Doi:10.15672/hujms.1173649

View : 103 | Download : 284

Publication Date : 2023-11-03

Article Type : Research Paper

Abstract :We study a nonlinear nonhomogeneous Dirichlet problem with a nonsmooth potential which is superlinear but without satisfying the Ambrosetti-Rabinowitz condition. Using the nonsmooth critical point theory and critical groups we prove two multiplicity theorems producing three and five solutions respectively. In the second multiplicity theorem, we provide sign information for all the solutions and the solutions are ordered.
Keywords : Hemivariational inequality, Clarke subdifferential, nonsmooth critical point theory, critical groups, nodal solutions

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