Superlinear elliptic hemivariational inequalities

Year 2023, , 1631 - 1657, 03.11.2023

Yunru Bai , Leszek Gasinski , Nikolaos Papageorgiou

https://doi.org/10.15672/hujms.1173649

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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