Topological degree and applications to elliptic problems with discontinuous nonlinearity

We develop a topological degree theory for a class of locally bounded weakly upper semicontinuous set-valued operators of generalized (S+) type in real reflexive separable Banach spaces, based on the Berkovits-Tienari degree. The method of approach is to use elliptic super-regularization by means of certain compact embeddings, instead of the Galerkin method. Applying the degree theory, we tackle an elliptic boundary value problem with discontinuous nonlinearity. c 2017 All rights reserved.