On the three ''essential'' critical values theorem (Q5949153)
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scientific article; zbMATH DE number 1673384
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the three ''essential'' critical values theorem |
scientific article; zbMATH DE number 1673384 |
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On the three ''essential'' critical values theorem (English)
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14 November 2001
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The aim of the paper is to extend the Krasnosel'skij ``three critical points theorem'' for nonsmooth functionals. For a previous smooth version see \textit{V. Moroz, A. Vignoli} and \textit{P. Zabreĭko} [Topol. Methods Nonlinear Anal. 11, No. 1, 103-113 (1998; Zbl 0920.58016)]. The author exploits some modifications of the essential critical value definition for nonsmooth functionals, and proves a ``three critical values theorem''. The main theorem is valid in reflexive Banach spaces, but the auxiliary statements contain a good many inaccuracies.
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three critical points theorem
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deformation lemma
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essential critical value
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Palais-Smale condition
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