Topological degree and applications to elliptic problems with discontinuous nonlinearity
In‐Sook Kim · The Journal of Nonlinear Sciences and Applications · 2017
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.