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Proceedings of the American Mathematical Society

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A note on the topological degree at a critical point of mountainpass-type


Author: Helmut Hofer
Journal: Proc. Amer. Math. Soc. 90 (1984), 309-315
MSC: Primary 58E05; Secondary 47H15
DOI: https://doi.org/10.1090/S0002-9939-1984-0727256-0
MathSciNet review: 727256
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Abstract: In this note we will show that the local degree at an isolated critical point given by the Ambrosetti-Rabinowitz mountainpass-theorem is $ - 1$ for a large class of functionals. This class includes for example those functionals arising in the study of second order elliptic equations.


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DOI: https://doi.org/10.1090/S0002-9939-1984-0727256-0
Keywords: Critical point theory, Leray-Schauder degree, nonlinear functional analysis
Article copyright: © Copyright 1984 American Mathematical Society