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arXiv · 2201.09272

An antimaximum principle for periodic solutions of a forced oscillator

Alain Albouy·Antonio J. Ureña
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Abstract

Consider the equation of the linear oscillator $u"+u=h(\theta)$, where the forcing term $h:\mathbb R\to\mathbb R$ is $2\pi$-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.

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Alain Albouy, Antonio J. Ureña. 2022-01-23. An antimaximum principle for periodic solutions of a forced oscillator. https://doi.org/10.1142/s0219199722500419

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