Leray-Schauder degree: a half century of extensions and applications
KeywordsLeray-Schauder degree, fixed point index, fixed point theorems, continuation theorems, bifurcation
AbstractThe 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.
How to Cite
MAWHIN, Jean. Leray-Schauder degree: a half century of extensions and applications. Topological Methods in Nonlinear Analysis. Online. 1 December 1999. Vol. 14, no. 2, pp. 195 - 228. [Accessed 4 October 2023].
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