In a previous paper, the first and third author developed a degree theory for oriented locally compact perturbations of C1 Fredholm maps of index zero between real Banach spaces. In the spirit of a celebrated Amann-Weiss paper, we prove that this degree is unique if it is assumed to satisfy three axioms: Normalization, Additivity and Homotopy invariance. Taking into account that any compact vector field has a canonical orientation, from our uniqueness result we shall deduce that the above degree provides an effective extension of the Leray-Schauder degree.

On the degree for oriented quasi-Fredholm maps: its uniqueness and its effective extension of the Leray--Schauder degree / Benevieri, Pierluigi; Furi, Massimo; Calamai, Alessandro. - In: TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS. - ISSN 1230-3429. - STAMPA. - 46:(2015), pp. 401-430. [10.12775/TMNA.2015.052]

On the degree for oriented quasi-Fredholm maps: its uniqueness and its effective extension of the Leray--Schauder degree

BENEVIERI, PIERLUIGI;FURI, MASSIMO;
2015

Abstract

In a previous paper, the first and third author developed a degree theory for oriented locally compact perturbations of C1 Fredholm maps of index zero between real Banach spaces. In the spirit of a celebrated Amann-Weiss paper, we prove that this degree is unique if it is assumed to satisfy three axioms: Normalization, Additivity and Homotopy invariance. Taking into account that any compact vector field has a canonical orientation, from our uniqueness result we shall deduce that the above degree provides an effective extension of the Leray-Schauder degree.
2015
46
401
430
Benevieri, Pierluigi; Furi, Massimo; Calamai, Alessandro
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/1056139
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