Boundedness of solutions of a quasi-periodic sublinear Duffing equation
type: Item
instance of: scholarly article
title: Boundedness of solutions of a quasi-periodic sublinear Duffing equation
zbMATH Open document ID: 1472.34066
author: Yaqun Peng
author: Xinli Zhang
author: Daxiong Piao
published in: Chinese Annals of Mathematics. Series B
publication date: 2021-05-06T00:00:00Z
review text: In this paper, the authors study the Lagrangian stability for the sublinear Duffing equations \(x''+e(t)|x|^{\alpha-1}x=p(t)\) with \(0<\alpha<1\), where \(e\) and \(p\) are real analytic quasi-periodic functions with frequency \(\omega\). By using the invariant curve theorem for quasi-periodic mappings established by \textit{P. Huang} et al. [Nonlinearity 29, No. 10, 3006--3030 (2016; Zbl 1378.37078)], they prove that every solution of the equation is bounded provided that the mean value of \(e\) is positive and the frequency \(\omega\) satisfies a Diophantine condition.
reviewed by: Zaihong Wang
Mathematics Subject Classification ID: 34C11
Mathematics Subject Classification ID: 37C60
Mathematics Subject Classification ID: 34C15
zbMATH DE Number: 7344775
zbMATH Keywords: Hamiltonian system
zbMATH Keywords: sublinear Duffing equation
zbMATH Keywords: boundedness
zbMATH Keywords: quasi-periodic solution
zbMATH Keywords: invariant curve
MaRDI profile type: Publication
full work available at URL: s11401-021-0246-9
OpenAlex ID: W3127362477
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DOI: 10.1007/S11401-021-0246-9
description: scientific article; zbMATH DE number 7344775