A hemivariational inequality involving pp-Laplacian on an infinite strip

This paper deals with an eigenvalue problem for hemivariational inequalities on domains of the type ω×Rω×R (ωω is a bounded open subset of RN−1RN−1, N≥2N≥2) 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 W01,p(ω×R) whenever the eigenvalues are of certain range. Our approach is variational based on the theories of non-smooth analysis. Our results are a generalization of the case of Laplacian from A. Kristály, et al. to the case of pp-Laplacian.