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

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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 Kristály, Lisei, and Varga [A. Kristály, H. Lisei, C. Varga, Multiple solutions for p -Laplacian type operator, Nonlinear Anal. 68 (5) (2008) 1375–1381].