Abstract and Applied Analysis

A degree theory for compact perturbations of proper $C^{1}$ Fredholm mappings of index $0$

Patrick J. Rabier and Mary F. Salter

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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.

Article information

Source
Abstr. Appl. Anal., Volume 2005, Number 7 (2005), 707-731.

Dates
First available in Project Euclid: 3 October 2005

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1128345977

Digital Object Identifier
doi:10.1155/AAA.2005.707

Mathematical Reviews number (MathSciNet)
MR2202179

Zentralblatt MATH identifier
1117.47049

Citation

Rabier, Patrick J.; Salter, Mary F. A degree theory for compact perturbations of proper $C^{1}$ Fredholm mappings of index $0$. Abstr. Appl. Anal. 2005 (2005), no. 7, 707--731. doi:10.1155/AAA.2005.707. https://projecteuclid.org/euclid.aaa/1128345977


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