Boundedness of solutions for a class of sublinear reversible oscillators with periodic forcing
type: Item
instance of: scholarly article
title: Boundedness of solutions for a class of sublinear reversible oscillators with periodic forcing
zbMATH Open document ID: 1296.34084
DOI: 10.1155/2013/246343
published in: Abstract and Applied Analysis
publication date: 2014-06-23T00:00:00Z
review text: Summary: We study the boundedness of all solutions for the differential equation \[ x''+f(x)x'+(B+\varepsilon e(t))|x|^{\alpha -1}x=p(t), \] where \(f(x)\), \(p(t)\) are odd functions, \(e(t)\) is an even function, \(e(t)\), \(p(t)\) are smooth 1-periodic functions, \(B\) is a nonzero constant, and \(\varepsilon\) is a small parameter. A sufficient and necessary condition for the boundedness of all solutions of the above equation is established. Moreover, the existence of Aubry-Mather sets is obtained as well.
Mathematics Subject Classification ID: 34C11
Mathematics Subject Classification ID: 34C15
Mathematics Subject Classification ID: 34C14
zbMATH DE Number: 6306558
Wikidata QID: Q58915650
author: Ting-Ting Zhang
author: Jianguo Si
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/246343
OpenAlex ID: W2041658866
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description: scientific article; zbMATH DE number 6306558