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Indice de Morse des points critiques obtenus par minimax. (The Morse index of critical points obtained by minimax). (French) Zbl 0695.58007

Summary: We give bounds for the Morse index of a critical point obtained by minimax on some homology class. This improves previous results in which the minimax was taken on a homotopy (resp. cohomotopy) class and one only obtains an upper (resp. lower) bound on the index [see for instance A. Bahri and P. L. Lions, C. R. Acad. Sci., Paris, Sér. I 301, 145-147 (1985; Zbl 0589.58007)].

MSC:

58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
57R45 Singularities of differentiable mappings in differential topology
57R70 Critical points and critical submanifolds in differential topology

Citations:

Zbl 0589.58007
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References:

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[2] Bahri, A.; Lions, P. L., Remarques sur la théorie variationnelle des points critiques et applications, C.R. Acad. Sci. Paris, t. 301, 145-147, (1985) · Zbl 0589.58007
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