A degree theory for compact perturbations of proper C1 Fredholm mappings of index 0

Patrick J. Rabier and Mary F. Salter

Abstract and Applied Analysis, 2005, vol. 2005, issue 7, 707-731

Abstract: We construct a degree for mappings of the form F + K between Banach spaces, where F is C1 Fredholm of index 0 and K is compact. This degree generalizes both the Leray‐Schauder degree when F = I and the degree for C1 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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https://doi.org/10.1155/AAA.2005.707

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2005:y:2005:i:7:p:707-731

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