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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| _version_ | 1850236854992896000 |
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| author | Patrick J. Rabier Mary F. Salter |
| author_facet | Patrick J. Rabier Mary F. Salter |
| author_sort | Patrick J. Rabier |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-11d99c2ed7f242e19405bc7c41f65216 |
| institution | OA Journals |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2005-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-11d99c2ed7f242e19405bc7c41f652162025-08-20T02:01:53ZengWileyAbstract and Applied Analysis1085-33751687-04092005-01-012005770773110.1155/AAA.2005.707A degree theory for compact perturbations of proper C1 Fredholm mappings of index 0Patrick J. Rabier0Mary F. Salter1Department of Mathematics, University of Pittsburgh, Pittsburgh 15260, PA, USADepartment of Mathematics and Computer Science, Franciscan University of Steubenville, Steubenville 43952, OH, USAWe 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.http://dx.doi.org/10.1155/AAA.2005.707 |
| spellingShingle | Patrick J. Rabier Mary F. Salter A degree theory for compact perturbations of proper C1 Fredholm mappings of index 0 Abstract and Applied Analysis |
| title | A degree theory for compact perturbations of proper
C1 Fredholm mappings of index 0 |
| title_full | A degree theory for compact perturbations of proper
C1 Fredholm mappings of index 0 |
| title_fullStr | A degree theory for compact perturbations of proper
C1 Fredholm mappings of index 0 |
| title_full_unstemmed | A degree theory for compact perturbations of proper
C1 Fredholm mappings of index 0 |
| title_short | A degree theory for compact perturbations of proper
C1 Fredholm mappings of index 0 |
| title_sort | degree theory for compact perturbations of proper c1 fredholm mappings of index 0 |
| url | http://dx.doi.org/10.1155/AAA.2005.707 |
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