An eigenvalue problem for hemivariational inequalities with combined nonlinearities on an infinite strip Original Research Article

In this paper a class of eigenvalue problems for hemivariational inequalities is studied which is defined on domains of the type ω×Rω×R (ωω is a bounded open subset of RmRm, m⩾1m⩾1) and it involves concave–convex nonlinearities. Under suitable conditions on the nonlinearities, two nontrivial solutions are obtained which belong to a special closed convex cone of View the MathML sourceH01(ω×R) whenever the eigenvalues are of certain range. Our approach is variational, the main tool in our investigation is the critical point theory developed by Motreanu and Panagiotopoulos [Minimax Theorems and Qualitative Properties of the Solutions of Hemivariational Inequalities, Kluwer Academic Publishers, Dordrecht, 1999, Chapter 3].