A degree theory for compact perturbations of proper C1 Fredholm mappings of index 0
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 prov...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2005-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/AAA.2005.707 |
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| Summary: | 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. |
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| ISSN: | 1085-3375 1687-0409 |