Periodic solutions of forced isochronous oscillators at resonance
by
Denis Bonheure
Université Catholique de Louvain
Coauthors: Christian Fabry (Université Catholique de Louvain), Didier Smets (Université Catholique de Louvain)

We study the existence of periodic solutions for forced nonlinear oscillators at resonance, the nonlinearity being a bounded perturbation of a function deriving from an isochronous potential, i.e. a potential leading to free oscillations that all have the same period. The family of isochronous oscillators considered here includes oscillators with jumping nonlinearities, as well as oscillators with a repulsive singularity, to which a particular attention is paid. Assuming that the forcing term p is T-periodic and that the minimal period of the free isochronous oscillations is T/k, for some integer k, the existence results are based on properties of the function \Phi(\theta) = \int₀^T/k p(t) \psi(t+\theta)  dt, where \psi is a solution of an asymptotic system approaching the isochronous oscillator for large amplitudes. The existence results contain, as particular cases, conditions of Landesman-Lazer type.

Date received: February 12, 2001

Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cafv-20.