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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles 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 min-max principle with a relaxed boundary condition
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by N. Ghoussoub PDF
Proc. Amer. Math. Soc. 117 (1993), 439-447 Request permission

Abstract:

A standard Min-Max procedure to find critical points for a ${C^1}$functional $\varphi$ verifying a compactness condition of Palais-Smale type on a smooth Banach manifold $X$ consists of finding an appropriate class $\mathcal {F}$ of compact subsets of $X$, all containing a fixed boundary $B$, and then showing that the value $c = {\inf _{A \in \mathcal {F}}}{\sup _{x \in A}}\varphi (x)$ is a critical level, provided it satisfies $\sup \varphi (B) < c$. In this paper, we refine this procedure by relaxing the boundary condition.
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Additional Information
  • © Copyright 1993 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 117 (1993), 439-447
  • MSC: Primary 58E05
  • DOI: https://doi.org/10.1090/S0002-9939-1993-1089405-2
  • MathSciNet review: 1089405