Boundedness of solutions in impulsive Duffing equations with polynomial potentials and C¹ time dependent coefficients

2017/06/18 by Yanmin Niu, Xiong Li, Niu, Yanmin +1
Mathematics · #Differential Equations and Numerical Methods #Dynamical Systems (math.DS) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1706.06460

openalex publication_date 2017/06/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we are concerned with the impulsive Duffing equation x''+x²ⁿ⁺¹+∑_i=0²ⁿxⁱp_i(t)=0, t≠ t_j, with impulsive effects x(t_j+)=x(t_j-), x'(t_j+)=-x'(t_j-), j=±1,±2,⋯, where the time dependent coefficients p_i(t)∈ C¹(\mathbbS¹) (n+1≤ i≤ 2n) and p_i(t)∈ C⁰(\mathbbS¹) (0≤ i≤ n) with \mathbbS¹=ℝ/ℤ. If impulsive times are 1-periodic and t₂-t₁≠(1)/(2) for 0< t₁

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