Boundedness of solutions for Duffing equation with low regularity in time

2017/05/08 by Xiaoping Yuan, Yuan, Xiaoping
Mathematics · #Differential Equations and Boundary Problems #Dynamical Systems (math.DS) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1705.02881

openalex publication_date 2017/05/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is shown that all solutions are bounded for Duffing equation x+ x²ⁿ⁺¹+∑_j=0²ⁿP_j(t)x^j=0, provided that for each n+1≤ j≤ 2n, P_j(t)∈ C^γ(\mathbb T) with γ>1-\frac1n and for each 0≤ j≤ n, P_j∈ L(\mathbb T¹).

Related

• Boundedness of solutions in impulsive Duffing equations with polynomial potentials and C¹ time dependent coefficients
• Boundedness of solutions for the reversible system with low regularity in time
• The large twist theorem and boundedness of solutions for polynomial potentials with C¹ time dependent coefficients
• Lagrange stability for impulsive Duffing equations
• Boundedness of semilinear Duffing equations at resonance with oscillating nonlinearities