Parameter diagram for global asymptotic stability of damped half-linear oscillators
type: Item
instance of: scholarly article
title: Parameter diagram for global asymptotic stability of damped half-linear oscillators
zbMATH Open document ID: 1344.34066
author: Wei Zheng
author: Jitsuro Sugie
published in: Monatshefte für Mathematik
publication date: 2016-02-01T00:00:00Z
review text: The authors consider a half-linear differential equation with an unbounded damping term \[ (\phi _p (x'))'+h(t)\phi _p (x')+\omega^p\phi _p(x)=0,\tag{1} \] where \(\omega > 0\), \(t \in \left[a,\infty\right),\) \[ \phi _p(z)=\begin{cases} |z|^{p-2}z,& \text{ if }z\neq 0, \\ 0, & \text{ if }z = 0 \end{cases} \] with \(p > 1\) and \(z \in\mathbb R\). The authors prove three new theorems which include certain new necessary and sufficient conditions to guarantee the global asymptotical stability of the equilibrium of equation (1). They also give parameter diagrams to clarify the relations between the index number \(p\) and the parameters. They extend and improve some results in the relevant literature.
reviewed by: Cemil Tunç
Mathematics Subject Classification ID: 34D23
Mathematics Subject Classification ID: 34D05
Mathematics Subject Classification ID: 34C15
zbMATH DE Number: 6537864
zbMATH Keywords: time-varying differential equation
zbMATH Keywords: unbounded damping
zbMATH Keywords: growth condition
zbMATH Keywords: improper integral
zbMATH Keywords: limit comparison test
MaRDI profile type: Publication
full work available at URL: s00605-014-0695-2
OpenAlex ID: W1999444144
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DOI: 10.1007/S00605-014-0695-2
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description: scientific article; zbMATH DE number 6537864