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Pré-Publication, Document De Travail Année : 2024

Monotonicity of the period and positive periodic solutions of a quasilinear equation

Résumé

We investigate the monotonicity of the minimal period of the periodic solutions of some quasilinear differential equations involving the p-Laplace operator. The monotonicity is obtained as a function of a Hamiltonian energy in two cases. We first extend to the case p≥2 classical results for p=2 due to Chow and Wang, and Chicone. Then we consider a differential equation associated with a fundamental interpolation inequality in Sobolev spaces. In that case, we generalize to p≥2 a recent result due to Benguria, Depassier and~Loss when p=2.
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Dates et versions

hal-03924391 , version 1 (05-01-2023)
hal-03924391 , version 2 (22-03-2023)
hal-03924391 , version 3 (27-11-2023)
hal-03924391 , version 4 (11-04-2024)

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  • HAL Id : hal-03924391 , version 4

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Jean Dolbeault, Marta García-Huidobro, Raúl Manásevich. Monotonicity of the period and positive periodic solutions of a quasilinear equation. 2024. ⟨hal-03924391v4⟩
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