Nonlinear oscillators at resonance with periodic forcing
Philip Korman, Yi Li
TL;DR
This paper unifies various results on nonlinear oscillators at resonance with periodic forcing, providing conditions for the existence and non-existence of solutions and describing the dynamics when solutions are absent.
Contribution
It consolidates multiple prior findings into a unified framework and offers detailed analysis of nonlinear oscillations at resonance, especially when periodic solutions do not exist.
Findings
Conditions for existence of periodic solutions
Conditions for non-existence of solutions
Detailed description of nonlinear dynamics at resonance
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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Taxonomy
TopicsNonlinear Differential Equations Analysis · Nonlinear Partial Differential Equations · Advanced Differential Equations and Dynamical Systems