A topological degree for operators of generalized $(S_{+})$ type
In-Sook Kim, Suk-Joon Hong · Fixed Point Theory and Applications · 2015
Abstract As an extension of the Leray-Schauder degree, we introduce a topological degree theory for a class of demicontinuous operators of generalized $(S_{+})$ ( S + ) type in real reflexive Banach spaces, based on the recent Berkovits degree. Using the degree theory, we show that the Borsuk theorem holds true for this class. Moreover, we study the Dirichlet boundary value problem involving the p -Laplacian by way of an abstract Hammerstein equation.