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arXiv · 2512.14940

Nonlinear oscillators at resonance with periodic forcing

Philip Korman·Yi Li
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Abstract

In this note we unify the results of A.C. Lazer and P.O. Frederickson [3], A.C. Lazer [6], A.C. Lazer and D.E. Leach [7], J.M. Alonso and R. Ortega [1], and P. Korman and Y. Li [4] on periodic oscillations and unbounded solutions of nonlinear equations with linear part at resonance and periodic forcing. We give conditions for the existence and non-existence of periodic solutions, and obtain a rather detailed description of the dynamics for nonlinear oscillations at resonance, in case periodic solutions do not exist.

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Philip Korman, Yi Li. 2025-12-16. Nonlinear oscillators at resonance with periodic forcing. https://arxiv.org/abs/2512.14940

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