A degree theory for compact perturbations of proper $C^{1}$ Fredholm mappings of index $0$
Rabier, Patrick J. ; Salter, Mary F.
Abstr. Appl. Anal., Tome 2005 (2005) no. 2, p. 707-731 / Harvested from Project Euclid
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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 $F(\lambda,x)+K(\lambda,x)=0$ .
Publié le : 2005-09-26
Classification:  
@article{1128345977,
     author = {Rabier, Patrick J. and Salter, Mary F.},
     title = {A degree theory for compact perturbations of proper
$C^{1}$ Fredholm mappings of index $0$},
     journal = {Abstr. Appl. Anal.},
     volume = {2005},
     number = {2},
     year = {2005},
     pages = { 707-731},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1128345977}
}

Rabier, Patrick J.; Salter, Mary F. A degree theory for compact perturbations of proper
$C^{1}$ Fredholm mappings of index $0$. Abstr. Appl. Anal., Tome 2005 (2005) no. 2, pp.  707-731. http://gdmltest.u-ga.fr/item/1128345977/