A necessary and sufficient condition for the asymptotic stability of the damped oscillator
type: Item
instance of: scholarly article
title: A necessary and sufficient condition for the asymptotic stability of the damped oscillator
zbMATH Open document ID: 0831.34052
author: Vilmos Totik
author: László Hatvani
author: Tibor Krisztin
published in: Journal of Differential Equations
publication date: 1995-07-25T00:00:00Z
review text: The authors are interested in the solution of an old problem ``to find the conditions on the damping coefficient \(h\) of the second order differential equation \(x'' + h(t)x' + k^2x = 0\) guaranteeing the asymptotic stability of the equilibrium \(x = x' = 0\).'' The authors prove by a very interesting method a new necessary and sufficient condition for the asymptotic stability and they deduce the relations between their results and the results of other authors.
Mathematics Subject Classification ID: 34D20
Mathematics Subject Classification ID: 34A30
zbMATH DE Number: 769002
zbMATH Keywords: damped linear oscillator
zbMATH Keywords: second order differential equation
zbMATH Keywords: asymptotic stability
MaRDI profile type: Publication
full work available at URL: jdeq.1995.1087
OpenAlex ID: W2086431711
DOI: 10.1006/JDEQ.1995.1087
description: scientific article; zbMATH DE number 769002