Degree theoretic methods in the study of positive solutions for nonlinear hemivariational inequalities

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In this paper we study the existence of positive solutions for nonlinear elliptic problems driven by the $p$-Laplacian differential operator and with a nonsmooth potential (hemivariational inequalities). The hypotheses, in the case $p=2$ (semilinear problems), incorporate in our framework of analysis the so-called asymptotically linear problems. The approach is degree theoretic based on the fixed-point index for nonconvex-valued multifunctions due to Bader [3].