Littlewood's problem for isochronous oscillators
type: Item
instance of: scholarly article
title: Littlewood's problem for isochronous oscillators
zbMATH Open document ID: 1194.34057
author: Denis Bonheure
author: Christian Fabry
published in: Archiv der Mathematik
publication date: 2009-11-25T00:00:00Z
review text: The authors deal with the boundedness of solutions of isochronous oscillators \[ x''+V'(x)=p(t),\tag{*} \] where \(p\) is \(T\)-periodic and \(V\) is a \(T\)-isochronous potential, meaning that all nontrivial solutions of \(x''+V'(x)=0\) are periodic, with minimal period \(T\). By exchanging the role of time variable and angular variable and using ``small twist theorem'', the authors prove that, if \(\Phi(t)=\int_0^Tp(t)\psi(t+\theta)dt\) is of constant sign, then all solutions of (*) are bounded.
reviewed by: Zaihong Wang
Mathematics Subject Classification ID: 34C11
Mathematics Subject Classification ID: 34C25
zbMATH DE Number: 5638428
zbMATH Keywords: isochronous oscillator
zbMATH Keywords: boundedness
zbMATH Keywords: Littlewood's problem
MaRDI profile type: Publication
full work available at URL: s00013-009-0031-6
OpenAlex ID: W2034290107
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DOI: 10.1007/S00013-009-0031-6
description: scientific article; zbMATH DE number 5638428