Invariant tori in nonlinear oscillations
type: Item
instance of: scholarly article
title: Invariant tori in nonlinear oscillations
zbMATH Open document ID: 0962.34027
DOI: 10.1007/BF02889506
author: Bin Liu
author: Yiqian Wang
published in: Science in China. Series A
publication date: 2001-06-14T00:00:00Z
review text: The boundedness of all solutions to the semilinear Duffing equation \[ x''+ \omega^2x+ \phi(x)= p(t),\quad \omega\in \mathbb{R}^+\setminus \mathbb{N}, \] where \(P(t)\) is a smooth \(2\pi\)-periodic function and \(\phi(x)\) is bounded, is investigated. Typically, the authors show that the solutions are all bounded if, additionally, \(\lim_{x\to\pm \infty} \phi(x)\) are both finite and different, and \(\lim_{x\to\pm\infty}x^5 \phi^{(5)}(x)= 0\). The proof of this theorem requires eight technical lemmas.
Mathematics Subject Classification ID: 34C11
Mathematics Subject Classification ID: 34C27
zbMATH DE Number: 1439355
zbMATH Keywords: invariant tori
zbMATH Keywords: semilinear Duffing equation
zbMATH Keywords: nonlinear oscillations
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02889506
OpenAlex ID: W2059919504
description: scientific article; zbMATH DE number 1439355