Bounded Palais-Smale mountain-pass sequences

L Jeanjean (1) , Jf Toland

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

Let I(lambda, .), lambda is an element of R, be a family of C-1-functionals having mountain-pass geometry. Under hypotheses which do not ensure that the mountain-pass level c(lambda) is a monotone function of lambda, it is shown that I(lambda, .) has a bounded Palais-Smale sequence at level c(lambda), for almost every lambda. (C) Academie des Sciences/Elsevier, Paris.

Domaines: Physique mathématique [math-ph]

L Jeanjean, Jf Toland. Bounded Palais-Smale mountain-pass sequences. Comptes rendus de l'Académie des sciences. Série I, Mathématique, 1998, 327 (1), pp.23--28. ⟨10.1016/S0764-4442(98)80097-9⟩. ⟨hal-00693972⟩