A degree theory for compact perturbations of proper C1 Fredholm mappings of index 0. (26th September 2005) - Rabier, Patrick J.; Salter, Mary F.
Abstract : We construct a degree for mappings of the formF + K between Banach spaces, whereF isC 1 Fredholm of index0 andK is compact. This degree generalizes both the Leray-Schauder degree whenF = I and the degree forC 1 Fredholm mappings of index0 whenK = 0 . To exemplify the use of this degree, we prove the "invariance-of-domain" property whenF + K is one-to-one and a generalization of Rabinowitz's global bifurcation theorem for equationsF ( λ, x ) + K ( λ, x ) = 0 .