ON NEUMANN ELLIPTIC PROBLEMS WITH DISCONTINUOUS NONLINEARITIES

Nikolaos Halidias

Address. National Technical University, Department of Mathematics, Zografou Campus, Athens 157 80, GREECE

E-mail: nick@math.ntua.gr

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.