Boundedness of semilinear Duffing equations at resonance with oscillating nonlinearities

2013/12/06 by Zhiguo Wang, Wang, Zhiguo, Daxiong Piao +3
Mathematics · Physics and Astronomy · #34C15 #70H08 #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Quantum chaos and dynamical systems #math.DS #msc:34C15 #msc:70H08

paper · pdf · doi:10.48550/arxiv.1312.1842

42 pages

arxiv created 2013/12/06 · openalex publication_date 2013/12/06 · arxiv updated 2013/12/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we prove the boundedness of all the solutions for the equation x+n²x+g(x)+ψ'(x)=p(t) with the Lazer-Leach condition on g and p, where n∈ \mathbbN⁺, p(t) and ψ'(x) are periodic and g(x) is bounded. For the critical situation that |∫₀^2πp(t)e^intdt |=2|g(+∞)-g(-∞)|, we also prove a sufficient and necessary condition for the boundedness if ψ'(x)≡0.

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