Lagrange stability for impulsive Duffing equations

2018/06/02 by Jianhua Sun, Sun, Jianhua, Xiaoping Yuan +2
Mathematics · #34B15 #34C25 #34D15 #Dynamical Systems (math.DS) #FOS: Mathematics #Fractional Differential Equations Solutions #Nonlinear Differential Equations Analysis #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1806.00577

openalex publication_date 2018/06/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This work discusses the boundedness of solutions for impulsive Duffing equation with time-dependent polynomial potentials. By KAM theorem, we prove that all solutions of the Duffing equation with low regularity in time undergoing suitable impulses are bounded for all time and that there are many (positive Lebesgue measure) quasi-periodic solutions clustering at infinity. This result extends some well-known results on Duffing equations to impulsive Duffing equations.

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