A multiplicity theorem for hemivariational inequalities with a p-Laplacian-like differential operator

摘要

We consider a parametric nonlinear elliptic inclusion with a multivalued p-Laplacian-like differential operator and a nonsmooth potential (hemivariational inequality). Using a variational approach based on the nonsmooth critical point theory, we show that for all the values of the parameter in an open half-line, the problem admits at least two nontrivial solutions. Our result extends a recent one by Kristaly, Lisei, and Varga [A. KristAly, H. Lisei, C. Varga, Multiple solutions for p-Laplacian type operator, Nonlinear Anal. 68 (5) (2008) 1375-1381]. (c) 2007 Elsevier Ltd. All rights reserved.