On the degree for oriented quasi-Fredholm maps: its uniqueness and its effective extension of the Leray-Schauder degree
DOI:
https://doi.org/10.12775/TMNA.2015.052Keywords
Topological degree, nonlinear Fredholm maps, Banach spaces, compact mapsAbstract
In a previous paper, the first and third author developed a~degree theory for oriented locally compact perturbations of $C\sp{1}$ 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.Downloads
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2015-09-01
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BENEVIERI, Pierluigi, CALAMAI, Alessandro and FURI, Massimo. On the degree for oriented quasi-Fredholm maps: its uniqueness and its effective extension of the Leray-Schauder degree. Topological Methods in Nonlinear Analysis. Online. 1 September 2015. Vol. 46, no. 1, pp. 401 - 430. [Accessed 19 September 2024]. DOI 10.12775/TMNA.2015.052.
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