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Bounded Palais-Smale mountain-pass sequences

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

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