A degree theory for compact perturbations of properC1Fredholm mappings of index0

摘要

We construct a degree for mappings of the formF+KbetweenBanach spaces, whereFisC1Fredholm of index0andKis compact. This degree generalizesboth the Leray-Schauder degree whenF=Iand the degree forC1Fredholm mappings of index0whenK=0. To exemplifythe use of this degree, we prove the “invariance-of-domain”property whenF+Kis one-to-one and a generalization ofRabinowitz's global bifurcation theorem for equationsF(λ,x)+K(λ,x)=0.