Title

Stability and Exact Multiplicity of Periodic Solutions of Duffing Equations with Cubic Nonlinearities

Document Type

Article

Publication Date

3-27-2007

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.