Periodic solutions of forced isochronous oscillators at resonance
(2002) Discrete and Continuous Dynamical Systems — Vol. 8, n° 4, p. 907-930 (2002)
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- Abstract
- We study the existence of 2pi-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. The existence results contain, as particular cases, conditions of Landesman-Lazer type. Even in the case of perturbed linear oscillators, they improve earlier results. Multiplicity and non-existence results are also given.
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Bonheure, D., Fabry, C., & Smets, D. (2002). Periodic solutions of forced isochronous oscillators at resonance. Discrete and Continuous Dynamical Systems, 8(4), 907-930. https://doi.org/10.3934/dcds.2002.8.907 (Original work published 2002)