A degree theory for compact perturbations of proper C 1 Fredholm mappings of index 0

Patrick J. Rabier and Mary F. Salter

Abstract and Applied Analysis, 2005, vol. 2005, 1-25

Abstract:

We construct a degree for mappings of the form F + K between Banach spaces, where F is C 1 Fredholm of index 0 and K is compact. This degree generalizes both the Leray-Schauder degree when F = I and the degree for C 1 Fredholm mappings of index 0 when K = 0 . To exemplify the use of this degree, we prove the “invariance-of-domain” property when F + K is one-to-one and a generalization of Rabinowitz's global bifurcation theorem for equations F ( λ , x ) + K ( λ , x ) = 0 .

Date: 2005
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:297487

DOI: 10.1155/AAA.2005.707

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