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A geometric description of the neighbourhood of a critical point given by the mountain-pass theorem. (English) Zbl 0573.58007
The author proves the existence of certain geometric types of critical points. In this respect he gives a more precise version of the well-known mountain pass lemma. For similar results see also P. Pucci and J. Serrin [J. Funct. Anal. 59, 185-210 (1984; Zbl 0564.58012)]. For an application to Hamiltonian systems see I. Ekeland and the author [Invent. Math. 81, 155-188 (1985)].
Reviewer: G.Warnecke

58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
55M25 Degree, winding number
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