Stability and exact multiplicity of periodic solutions of Duffing equations with cubic nonlinearities
Classical Analysis and ODEs
2007-05-23 v1
Abstract
We study the stability and exact multiplicity of periodic solutions of the Duffing equation with cubic nonlinearities. We obtain sharp bounds for h such that the equation has exactly three ordered T-periodic solutions. Moreover, when h is within these bounds, one of the three solutions is negative, while the other two are positive. The middle solution is asymptotically stable, and the remaining two are unstable.
Keywords
Cite
@article{arxiv.math/0703818,
title = {Stability and exact multiplicity of periodic solutions of Duffing equations with cubic nonlinearities},
author = {Hongbin Chen and Yi Li},
journal= {arXiv preprint arXiv:math/0703818},
year = {2007}
}
Comments
Keywords: Duffing equation; Periodic solution; Stability