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

2023/01/05 by Jean Dolbeault, Dolbeault, Jean, Marta García‐Huidobro +3
Mathematics · #34C23 #34C25 #34L30 #35J92 #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #FOS: Mathematics #Nonlinear Differential Equations Analysis

paper · pdf · doi:10.48550/arxiv.2301.01992

openalex publication_date 2023/01/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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≥2 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≥2.

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