Eigenvalue Problems with Symmetries

In this Chapter we consider several classes of inequality problems involving hemivariational inequalities with various kinds of symmetry and possibly with constraints. We establish multiplicity results, including cases of infinitely many solutions. The proofs use powerful tools of non-smooth critical point theory combined with arguments from Algebraic Topology. Results in this direction in the framework of elliptic equations have been initially established by Ambrosetti and Rabinowitz (see [1], [16]), while pioneering results in the study of multiple solutions for periodic problems can be found in Fournier and Willem [6], and Mawhin and Willem [9].