TWIN POSITIVE SOLUTIONS FOR p-LAPLACIAN NONLINEAR NEUMANN PROBLEMS VIA VARIATIONAL AND DEGREE THEORETICAL METHODS

We consider a nonlinear Neumann problem driven by the p-Laplacian and with a nonsmooth potential function (hemivariational inequality). Using a combination of variational and degree theoretic techniques, we show that the problem has two positive smooth solutions. We also show the equivalence of W-n(1,p) and C-n(1) minimizers for a large class of locally Lipschitz functionals.