English

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.

Keywords

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

R2 v1 2026-07-01T08:28:17.425Z