On the three ”essential” critical values theorem. (English) Zbl 0987.58005
The aim of the paper is to extend the Krasnosel’skij “three critical points theorem” for nonsmooth functionals. For a previous smooth version see V. Moroz, A. Vignoli and 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.
Reviewer: Serghey G.Suvorov (Donetsk)
MSC:
| 58E05 | Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces |
Keywords:
three critical points theorem; deformation lemma; essential critical value; Palais-Smale conditionCitations:
Zbl 0920.58016References:
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