We consider a nonlinear Neumann problem driven by the $p$-Laplacian differential operator and with a nonsmooth potential function (hemivariational inequality). Using a degree-theoretic approach based on the degree map for certain multivalued perturbations of $(S)_+$-operators, we prove the existence of a nontrivial smooth solution.
"Solutions for nonlinear Neumann problems via degree theory for multivalued perturbations of $(S)_+$ maps." Adv. Differential Equations 11 (9) 961 - 980, 2006.