Archivio Istituzionale della RicercaWe construct a new integer valued degree theory for proper C2 Fredholm maps of index 0, defined on a simply connected domain. The degree depends on the choice of a point in the domain called "base point". However the change of the base point at most can change the sign of the degree. Also the degree is invariant by homotopy only up to a sig. However the change in degree in both cases is computable using a homotopy invariant of paths of Fredholm operators called parity. We use this in order to extend the Krasnoselskii-Rabinowitz global bifurcation theorem to Fredholm maps.
Degree theory for proper C^2-Fredholm maps I / Pejsachowicz, Jacobo; Fitzpatrick, P.; Rabier, P.. - In: JOURNAL FÜR DIE REINE UND ANGEWANDTE MATHEMATIK. - ISSN 0075-4102. - 427:(1992), pp. 1-33.
Degree theory for proper C^2-Fredholm maps I.
PEJSACHOWICZ, JACOBO;
1992
Abstract
We construct a new integer valued degree theory for proper C2 Fredholm maps of index 0, defined on a simply connected domain. The degree depends on the choice of a point in the domain called "base point". However the change of the base point at most can change the sign of the degree. Also the degree is invariant by homotopy only up to a sig. However the change in degree in both cases is computable using a homotopy invariant of paths of Fredholm operators called parity. We use this in order to extend the Krasnoselskii-Rabinowitz global bifurcation theorem to Fredholm maps.
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https://hdl.handle.net/11583/1403886
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