caa a22 4500 388109165 CHVBK 20180307125348.0 cr unu---uuuuu 161130s1999 xx s 000 0 eng 10.1017/S0308210500013147 doi S0308210500013147 pii (NATIONALLICENCE)cambridge-10.1017/S0308210500013147 Jeanjean Louis Université de Marne-La-Vallée, Equipe d'Analyse et de Mathématiques Appliquées, 5, bd Descartes, Champs-sur-Marne, 77454 Marne-La-Vallée Cedex 2, France (jeanjean@math.univ-mlv.fr) On the existence of bounded Palais-Smale sequences and application to a Landesman-Lazer-type problem set on ℝN [Elektronische Daten] [Louis Jeanjean] Using the ‘monotonicity trick' introduced by Struwe, we derive a generic theorem. It says that for a wide class of functionals, having a mountain-pass (MP) geometry, almost every functional in this class has a bounded Palais-Smale sequence at the MP level. Then we show how the generic theorem can be used to obtain, for a given functional, a special Palais-Smale sequence possessing extra properties that help to ensure its convergence. Subsequently, these abstract results are applied to prove the existence of a positive solution for a problem of the form We assume that the functional associated to (P) has an MP geometry. Our results cover the case where the nonlinearity f satisfies (i) f(x, s)s−1 → a ∈)0, ∞) as s →+∞; and (ii) f(x, s)s-1 is non decreasing as a function of s ≥ 0, a.e. x → ℝN. Copyright © Royal Society of Edinburgh 1999 Proceedings of the Royal Society of Edinburgh: Section A Mathematics Royal Society of Edinburgh Scotland Foundation 129/4(1999), 787-809 0308-2105 129:4<787 1999 129 PRM https://doi.org/10.1017/S0308210500013147 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0308210500013147 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Jeanjean Louis Université de Marne-La-Vallée, Equipe d'Analyse et de Mathématiques Appliquées, 5, bd Descartes, Champs-sur-Marne, 77454 Marne-La-Vallée Cedex 2, France (jeanjean@math.univ-mlv.fr) NATIONALLICENCE 773 0- Proceedings of the Royal Society of Edinburgh: Section A Mathematics Royal Society of Edinburgh Scotland Foundation 129/4(1999), 787-809 0308-2105 129:4<787 1999 129 PRM CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge