Topological Methods in Nonlinear Analysis

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

Jean Mawhin

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Abstract

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.

Article information

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

Dates
First available in Project Euclid: 29 September 2016

Permanent link to this document
https://projecteuclid.org/euclid.tmna/1475179840

Mathematical Reviews number (MathSciNet)
MR1766190

Zentralblatt MATH identifier
0957.47045

Citation

Mawhin, Jean. Leray-Schauder degree: a half century of extensions and applications. Topol. Methods Nonlinear Anal. 14 (1999), no. 2, 195--228. https://projecteuclid.org/euclid.tmna/1475179840


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