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• W1982258462 startingPage "787" @default.
• W1982258462 abstract "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 → ℝ N ." @default.
• W1982258462 created "2016-06-24" @default.
• W1982258462 creator A5078558982 @default.
• W1982258462 date "1999-01-01" @default.
• W1982258462 modified "2023-10-16" @default.
• W1982258462 title "On the existence of bounded Palais–Smale sequences and application to a Landesman–Lazer-type problem set on <i>ℝ^N</i>" @default.
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• W1982258462 doi "https://doi.org/10.1017/s0308210500013147" @default.
• W1982258462 hasPublicationYear "1999" @default.
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