A variational approach to resonance for asymmetric oscillators

Bonheure, Denis;Fabry, Christian
(2007) Communications on Pure and Applied Analysis — Vol. 6, n° 1, p. 163-181 (2007)

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  • Bonheure, Denis
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  • Fabry, ChristianUCLouvain
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Abstract
We consider in this note the equation x" + ax(+) - beta x(-) + g(x) - p(t), where x(+) = max{x, 0} is the positive part of x, x(-) = max{-x, 0} its negative part and alpha, beta are positive parameters. We assume that g : R --> R is continuous and bounded on R, p : R --> R is continuous and 2 pi-periodic. We provide some sufficient conditions of Ahmad, Lazer and Paul type for the existence of 2 pi-periodic solutions when (alpha, beta) belongs to one of the curves of the Fucik spectrum corresponding to 2 pi-periodic boundary conditions.
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Bonheure, D., & Fabry, C. (2007). A variational approach to resonance for asymmetric oscillators. Communications on Pure and Applied Analysis, 6(1), 163-181. https://hdl.handle.net/2078.5/135106 (Original work published 2007)