1999/03/31 by Youssef Jabri, Jabri, Youssef, Mimoun Moussaoui +1
Computer Science · Mathematics · #35A15 #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations #Optimization and Variational Analysis #math.AP #math.FA #msc:35A15
paper · pdf · doi:10.48550/arxiv.math/9903189
17 pages, part of the thesis of the first author (July 1995)
arxiv created 1999/03/31 · openalex publication_date 1999/03/31 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We give a linking theorem that strengthens and unifies some many minimax theorems including Ambrosetti-Rabinowitz ``mountain pass theorem'', Rabinowitz ``multidimensional mountain pass theorem'', Rabinowitz ``saddle point theorem'' and Silva's variants of these results. We focus our attention especially on ``the limiting case'', known to be true for the mountain pass principle, where some information on the location of the critical points is given. Two forms of this theorem are given: the first one is established via a deformation lemma and we use Ekeland's variational principle to get the second one.