Boundedness of solutions in a class of Duffing equations with a bounded restore force
type: Item
instance of: scholarly article
title: Boundedness of solutions in a class of Duffing equations with a bounded restore force
zbMATH Open document ID: 1109.34028
published in: Discrete and Continuous Dynamical Systems
publication date: 2006-03-29T00:00:00Z
review text: The equation \[ \frac{d^2x}{dt^2}+\arctan(x)=p(t), \] with \(p\in C^5\), \(p(t)=p(t+1)\), \(|\int^1_0p(t)\,dt|<\frac{\pi}{2}\), is considered. The boundedness of solutions, i.e., \(\sup_{t\in \mathbb{R}}(|x(t)|,|x'(t)|)<+\infty\), is proved by a series of transformations leading the equation to an appropriate form of KAM theory.
reviewed by: Péter F. Moson
Mathematics Subject Classification ID: 34C11
Mathematics Subject Classification ID: 34C27
zbMATH DE Number: 5015926
zbMATH Keywords: boundedness of solutions
zbMATH Keywords: bounded restore force
zbMATH Keywords: KAM theorem
author: Yiqian Wang
MaRDI profile type: Publication
full work available at URL: dcds.2006.14.783
OpenAlex ID: W2084310421
DOI: 10.3934/DCDS.2006.14.783
description: scientific article; zbMATH DE number 5015926