Double Eigenvalue Problems for Hemivariational Inequalities

Abstract

The aim of the present paper is to study a new type of eigenvalue problem, called a double eigenvalue problem, which arises in hemivariational inequalities related to nonconvex nonsmooth energy functionals. The paper provides existence results as well as some qualitative properties for the solutions to double eigenvalue problems for hemivariational inequalities under the presence of given nonlinear compact operators which are not necessarily of a variational structure. It presents three different approaches to such problems: minimization, minimax methods and (sub) critical point theory on a sphere. Applications illustrate the theory.