Abstract
We construct a degree for mappings of the form between Banach spaces, where is Fredholm of index and is compact. This degree generalizes both the Leray-Schauder degree when and the degree for Fredholm mappings of index when . To exemplify the use of this degree, we prove the “invariance-of-domain” property when is one-to-one and a generalization of Rabinowitz's global bifurcation theorem for equations .
Citation
Patrick J. Rabier. Mary F. Salter. "A degree theory for compact perturbations of proper $C^{1}$ Fredholm mappings of index $0$." Abstr. Appl. Anal. 2005 (7) 707 - 731, 26 September 2005. https://doi.org/10.1155/AAA.2005.707
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