A note on degree theory for gradient mappings

Amann, Herbert

doi:10.1090/S0002-9939-1982-0660610-2

A note on degree theory for gradient mappings
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by Herbert Amann PDF

Proc. Amer. Math. Soc. 85 (1982), 591-595 Request permission

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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Untere Schranken für die Anzahl von Lösungen einer Klasse nichtlinearer Dirichlet-probleme

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