Abstract. In this paper we study a class of nonlinear Neumann
elliptic problems with discontinuous nonlinearities.
We examine elliptic problems with multivalued boundary conditions involving the subdifferential of a locally
Lipschitz function in the sense of Clarke.
AMSclassification. 35J15, 35J20
Keywords. Neumann elliptic problems, variational method, locally Lipschitz functional, $p$-Laplacian.