A topological degree for operators of generalized $(S_{+})$ type
A topological degree for operators of generalized $(S_{+})$ type
Abstract As an extension of the Leray-Schauder degree, we introduce a topological degree theory for a class of demicontinuous operators of generalized $(S_{+})$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mo>(</mml:mo> <mml:msub> <mml:mi>S</mml:mi> <mml:mo>+</mml:mo> </mml:msub> <mml:mo>)</mml:mo> </mml:math> type in real reflexive Banach spaces, based on the recent Berkovits degree. Using the degree theory, we show …