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

In this paper a class of eigenvalue problems for hemivariational inequalities is studied which is defined on domains of the type ω×R (ω is a bounded open subset of Rm, m⩾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 H01(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].