Carletti, Timoteo

Villari, Gabriele

Zanolin, Fabio

English

We study the problem of existence of harmonic solutions for some generalisations of the periodically perturbed Liénard equation, where the damping function depends both on the position and the velocity. In the associated phase-space this corresponds to a term of the form f(x, y) instead of the standard dependence on x alone. We introduce suitable autonomous systems to control the orbits behaviour, allowing thus to construct invariant regions in the extended phase-space and to conclude about the existence of the harmonic solution, by invoking the Brouwer fixed point Theorem applied to the Poincaré map. Applications are given to the case of the p-Laplacian and the prescribed curvature equation

Repository of the University of Namur

Existence of harmonic solutions for some generalisation of the non-autonomous Liénard equations

https://pure.unamur.be/ws/files/62313822/CarlettiVillariZanolinNonAuto_1.pdf

Existence of harmonic solutions for some generalisation of the non-autonomous Liénard equations

Abstract

Similar works

Full text

Available Versions

Repository of the University of Namur

Repository of the University of Namur