Minimax Theorems and Qualitative Properties of the Solutions of Hemivariational Inequalities

This edition studies a new type of eigenvalue problem, one that is useful for applications: eigenvalue problems related to hemivariational inequalities, that is involving nonsmooth, nonconvex, energy functions. New existence, multiplicity and perturbation results are proved using three different approaches: minimization, minimax methods and (sub)critical point theory. Nonresonant and resonant cases are studied both for static and dynamic problems and several new qualitative properties of the hemivariational inequalities are obtained. Both simple and double eigenvalue problems are studied, as well as those constrained on the sphere and those which are unconstrained.