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arXiv · 2301.01992

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

Jean Dolbeault·Marta García-Huidobro·Raúl Manásevich
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Abstract

We investigate the monotonicity of the minimal period of periodic solutions of quasilinear differential equations involving the $p$-Laplace operator. First, the monotonicity of the period is obtained as a function of a Hamiltonian energy in two cases. We extend to $p\ge2$ classical results due to Chow-Wang and Chicone for $p=2$. Then we consider a differential equation associated with a fundamental interpolation inequality in Sobolev spaces. In that case, we generalize monotonicity results by Miyamoto-Yagasaki and Benguria-Depassier-Loss to $p\ge2$.

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Jean Dolbeault, Marta García-Huidobro, Raúl Manásevich. 2023-01-05. Monotonicity of the period and positive periodic solutions of a quasilinear equation. https://arxiv.org/abs/2301.01992

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