The Lagrangian stability for a class of second-order quasi-periodic reversible systems
type: Item
instance of: scholarly article
title: The Lagrangian stability for a class of second-order quasi-periodic reversible systems
zbMATH Open document ID: 1234.34032
DOI: 10.1155/2011/489148
author: Yanling Shi
author: J. Li
published in: Abstract and Applied Analysis
publication date: 2012-01-16T00:00:00Z
review text: Summary: We study the following second-order differential equation \[ (\Phi_p(x'))' + f(x, t) \Phi_p(x') + g(x, t) = 0, \] where \(\Phi_p(s) = |s|^{(p-2)} s\), \(p > 0\). \(f(x, t)\) and \(g(x, t)\) are real analytic functions in \(x\) and \(t\), \(2a\pi_p\)-periodic in \(x\), and quasi-periodic in \(t\) with frequencies \((\omega_1, \dots, \omega_m)\). Under some odd-even property of \(f(x, t)\) and \(g(x, t)\), we obtain the existence of invariant curves for above equation by a variant of the small twist theorem. Then, all solutions for the above equation are bounded in the sense of \(\text{sup}_{t \in\mathbb R}|x'(t)| < + \infty\).
Mathematics Subject Classification ID: 34C45
Mathematics Subject Classification ID: 34C15
Mathematics Subject Classification ID: 34D20
Mathematics Subject Classification ID: 34C14
Mathematics Subject Classification ID: 34C11
Mathematics Subject Classification ID: 37E40
zbMATH DE Number: 5997800
Wikidata QID: Q58654243
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2011/489148
OpenAlex ID: W2127356819
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description: scientific article; zbMATH DE number 5997800