Lyapunov stability for regular equations and applications to the Liebau phenomenon
type: Item
instance of: scholarly article
title: Lyapunov stability for regular equations and applications to the Liebau phenomenon
zbMATH Open document ID: 1477.34067
author: Feng Wang
author: J. Ángel Cid
author: Mirosława Zima
published in: Discrete and Continuous Dynamical Systems
publication date: 2018-08-16T00:00:00Z
review text: Recently, some results on the existence and stability of positive periodic solutions for the following singular second-order differential equation \[ \ddot{u}+a\dot{u}=\frac{1}{u}(e(t)-b(t)\dot{u}^2)-c \] with friction have been presented. However, there are few works on the conservative case \(a = 0\), which is an idealization but it is interesting from both the mathematical and the physical point of view. By means of classical topological techniques like the Kolmogorov-Arnold-Moser (KAM) theory, the Moser twist theorem, the averaging method and the method of upper and lower solutions in the reversed order, the authors study the existence and stability of periodic solutions of two kinds of regular equations for this gap. As an application, they present some results on the existence and stability of T-periodic solutions of a Liebau-type equation.
reviewed by: Ziheng Zhang
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 34B18
Mathematics Subject Classification ID: 34D20
Mathematics Subject Classification ID: 34B60
Mathematics Subject Classification ID: 37J40
zbMATH DE Number: 6919436
zbMATH Keywords: Lyapunov stability
zbMATH Keywords: regular equation
zbMATH Keywords: Liebau phenomenon
zbMATH Keywords: KAM theory
zbMATH Keywords: Moser twist theorem
MaRDI profile type: Publication
full work available at URL: dcds.2018204
OpenAlex ID: W2809421136
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DOI: 10.3934/DCDS.2018204
description: scientific article; zbMATH DE number 6919436