Nonlinear oscillators at resonance with periodic forcing
Dynamical Systems
2025-12-18 v1 Mathematical Physics
Analysis of PDEs
Classical Analysis and ODEs
math.MP
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.
Cite
@article{arxiv.2512.14940,
title = {Nonlinear oscillators at resonance with periodic forcing},
author = {Philip Korman and Yi Li},
journal= {arXiv preprint arXiv:2512.14940},
year = {2025}
}
Comments
8 pages, comments are welcome