JournalsaihpcVol. 6, No. 5pp. 321–330

A general mountain pass principle for locating and classifying critical points

  • N. Ghoussoub

    Department of Mathematics, University of British Columbia, Vancouver, Canada V6T 1Y4
  • D. Preiss

    Charles University, Prague, Czechoslovakia
A general mountain pass principle for locating and classifying critical points cover
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Abstract

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.

Résumé

On démontre une extension du théorème de col d’Ambrosetti-Rabinowitz dans laquelle une information auxiliaire sur la position du point critique est établie. On en déduit, d’une part, des résultats nouveaux, notamment le cas « limite » et d’autre part des démonstrations simples de résultats récents de Hofer et Pucci-Serrin sur la structure de l’ensemble critique.

Cite this article

N. Ghoussoub, D. Preiss, A general mountain pass principle for locating and classifying critical points. Ann. Inst. H. Poincaré Anal. Non Linéaire 6 (1989), no. 5, pp. 321–330

DOI 10.1016/S0294-1449(16)30313-4