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An antimaximum principle for periodic solutions of a forced oscillator

IMCCE, CNRS-UMR8028, Observatoire de Paris, 77, Avenue Denfert-Rochereau, 75014 Paris, France

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Departamento de Matematica Aplicada, Facultad de Ciencias, Campus Universitario de Fuentenueva, Universidad de Granada, 18071, Granada, Spain

E-mail Address: ajurena@ugr.es

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https://doi.org/10.1142/S0219199722500419Cited by:0 (Source: Crossref)

Abstract

Consider the equation of the linear oscillator $u^{″} + u = h (𝜃)$ , where the forcing term $h : ℝ \to ℝ$ is $2 π$ -periodic and positive. We show that the existence of a periodic solution implies the existence of a positive solution. To this aim we establish connections between this problem and some separation questions of convex analysis.

Keywords:

AMSC: 70J35, 26B25, 34A30

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