Multiple Solutions of Eigenvalue Problems for Hemivariational Inequalities

Abstract

The present chapter deals with multiplicity results for the eigenvalue problems of hemivariational inequalities. First we give a general minimax approach which permits the use of the corresponding linear eigenvalue problem for the determination of eigenvectors of a hemivariational inequality. Then the case of even nonconvex superpotential j(x, ·) is studied by using some elements of the theory of genus of Krasnosel’skii. For the sake of completeness we recall some elements of the theory of genus and we apply them to the proof of the corresponding multiplicity results. The results of this chapter are applied to some problems of Mechanics and Engineering Sciences. Note that Section 5.1 deals with the λ(V, H) eigenvalue problem, where Sections 5.2, 5.3, 5.4 with the λ(L 2, V) eigenvalue problem. (Here H ⊂ V (resp. V ⊂ L 2) are Hilbert spaces).