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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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.
References
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Additional 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