A note on degree theory for gradient mappings
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- by Herbert Amann
- Proc. Amer. Math. Soc. 85 (1982), 591-595
- DOI: https://doi.org/10.1090/S0002-9939-1982-0660610-2
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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.References
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Bibliographic Information
- © Copyright 1982 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 85 (1982), 591-595
- MSC: Primary 47H15; Secondary 58E05
- DOI: https://doi.org/10.1090/S0002-9939-1982-0660610-2
- MathSciNet review: 660610