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Proceedings of the American Mathematical Society

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

 
 

 

A min-max principle with a relaxed boundary condition


Author: N. Ghoussoub
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
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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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DOI: https://doi.org/10.1090/S0002-9939-1993-1089405-2
Article copyright: © Copyright 1993 American Mathematical Society

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