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A general mountain pass principle for locating and classifying critical points. (English) Zbl 0711.58008
Summary: A general “Mountain pass” principle that extends the theorem of Ambrosetti-Rabinowitz and which gives more information about the location of critical points, is established. This theorem also covers the problem of the “limiting case”, i.e. when “the separating mountain range has zero altitude”. It is also shown how this principle yields localized versions of recent results of Hofer and Pucci-Serrin concerning the structure of the critical set.

MSC:
58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
49J35 Existence of solutions for minimax problems
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References:
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