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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A note on degree theory for gradient mappings


Author: Herbert Amann
Journal: Proc. Amer. Math. Soc. 85 (1982), 591-595
MSC: Primary 47H15; Secondary 58E05
MathSciNet review: 660610
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Abstract: In this note we give a simple proof for the essentially known fact, that the Leray-Schauder degree of the gradient of a coercive functional on a large ball of a Hilbert space is one. As a simple application we show that the local index of an isolated local minimum of a $ {C^1}$-functional on a Hilbert space equals one.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1982-0660610-2
PII: S 0002-9939(1982)0660610-2
Keywords: Leray-Schauder degree, critical point theory, nonlinear functional analysis
Article copyright: © Copyright 1982 American Mathematical Society