Open Access
Translator Disclaimer
26 September 2005 A degree theory for compact perturbations of proper $C^{1}$ Fredholm mappings of index $0$
Patrick J. Rabier, Mary F. Salter
Abstr. Appl. Anal. 2005(7): 707-731 (26 September 2005). DOI: 10.1155/AAA.2005.707

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.

Citation

Download 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

Information

Published: 26 September 2005
First available in Project Euclid: 3 October 2005

zbMATH: 1117.47049
MathSciNet: MR2202179
Digital Object Identifier: 10.1155/AAA.2005.707

Rights: Copyright © 2005 Hindawi

JOURNAL ARTICLE
25 PAGES


SHARE
Vol.2005 • No. 7 • 26 September 2005
Back to Top