Topological Methods in Nonlinear Analysis

Leray-Schauder degree: a half century of extensions and applications

Jean Mawhin

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The Leray-Schauder degree is defined for mappings of the form $I-C$, where $C$ is a compact mapping from the closure of an open bounded subset of a Banach space $X$ into $X$. Since the fifties, a lot of work has been devoted in extending this theory to the same type of mappings on some nonlinear spaces, and in extending the class of mappings in the frame of Banach spaces or manifolds. New applications of Leray-Schauder theory and its extensions have also been given, specially in bifurcation theory, nonlinear boundary value problems and equations in ordered spaces. The paper surveys those developments.

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Topol. Methods Nonlinear Anal., Volume 14, Number 2 (1999), 195-228.

First available in Project Euclid: 29 September 2016

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Mawhin, Jean. Leray-Schauder degree: a half century of extensions and applications. Topol. Methods Nonlinear Anal. 14 (1999), no. 2, 195--228.

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