%0 Unpublished work %T Monotonicity of the period and positive periodic solutions of a quasilinear equation %+ CEntre de REcherches en MAthématiques de la DEcision (CEREMADE) %+ Pontificia Universidad Católica de Chile (UC) %+ Universidad de Chile = University of Chile [Santiago] (UCHILE) %+ Centre de modélisation mathématique (CMM) %A Dolbeault, Jean %A García-Huidobro, Marta %A Manásevich, Raúl %Z Fondecyt grants 1210241 and 1190102 from ANID-Chile %Z Centro de Modelamiento Matemático (CMM) BASAL fund FB210005 for center of excellence from ANID-Chile %8 2023-03-22 %D 2023 %K Hamiltonian systems %K quasilinear elliptic equations %K p-Laplace operator %K periodic solutions %K period %K energy levels %Z 34C25; 35J92; 34L30; 34C23 %Z Mathematics [math]/Analysis of PDEs [math.AP]Preprints, Working Papers, ... %X 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. %G English %2 https://hal.science/hal-03924391v2/document %2 https://hal.science/hal-03924391v2/file/DGHM2023.pdf %L hal-03924391 %U https://hal.science/hal-03924391 %~ CNRS %~ UNIV-DAUPHINE %~ INSMI %~ CEREMADE %~ TDS-MACS %~ PSL %~ UNIV-DAUPHINE-PSL %~ ANR