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

Jean Dolbeault (1) , Marta García-Huidobro (2) , Raúl Manásevich (3, 4)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 UC - Pontificia Universidad Católica de Chile
3 UCHILE - Universidad de Chile = University of Chile [Santiago]
4 CMM - Centre de modélisation mathématique / Centro de Modelamiento Matemático [Santiago]

We investigate the monotonicity of the minimal period of the periodic solutions of some quasilinear differential equations and extend results for p = 2 due to Chow and Wang, and to Chicone, to the case of the p-Laplace operator. Our main result is the monotonicity of the period for positive solutions of a nonlinear Euler-Lagrange equation for a minimization problem related with a fundamental interpolation inequality. In particular we generalize to p greater than 2 recent results of Benguria, Depassier and Loss.

Mots clés: Hamiltonian systems; quasilinear elliptic equations; p-Laplace operator; periodic solutions; period; energy levels

Domaines: Equations aux dérivées partielles [math.AP]

Jean Dolbeault, Marta García-Huidobro, Raúl Manásevich. Monotonicity of the period and positive periodic solutions of a quasilinear equation. 2023. ⟨hal-03924391v1⟩