Stability and exact multiplicity of periodic solutions of Duffing equations with cubic nonlinearities

2007/03/27 by Hongbin Chen, Yi Li, Chen, Hongbin +1
Mathematics · #34C10 #34C25 #Advanced Differential Equations and Dynamical Systems #Classical Analysis and ODEs (math.CA) #Differential Equations and Numerical Methods #FOS: Mathematics #Nonlinear Differential Equations Analysis #math.CA #msc:34C10 #msc:34C25

paper · pdf · doi:10.48550/arxiv.math/0703818

Keywords: Duffing equation; Periodic solution; Stability

arxiv created 2007/03/27 · openalex publication_date 2007/03/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

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.

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