Linearization of second-order superlinear oscillation theorems
type: Item
instance of: scholarly article
title: Linearization of second-order superlinear oscillation theorems
zbMATH Open document ID: 1073.34032
DOI: 10.1016/S0895-7177(04)90538-9
author: Ravi P. Agarwal
author: Said R. Grace
author: Donal O'Regan
published in: Mathematical and Computer Modelling
publication date: 2005-02-22T00:00:00Z
review text: The authors present comparison theorems for oscillation of second-order superlinear differential equations. The main results involve the comparison with related linear and half-linear second-order differential equations, so that the known oscillation theorems from literature can be employed directly. A typical result is the following one: Assume that \[ \int_{t_0}^{\infty} a^{-1/\alpha}(s)ds = \infty \] and \[ f^{(1/\alpha)-1}(x)f'(x)\geq k>0, \] for \(x\neq 0\), where \(k\) is a constant. If the half-linear equation \[ (a(t)| y'(t)| ^{\alpha-1}y'(t))'+\left(\frac k{\alpha}\right)q(t)| y(t)| ^{\alpha-1}y(t)=0 \] is oscillatory, then the superlinear equation \[ (a(t)| x'(t)| ^{\alpha-1}x'(t))'+q(t)f(x(t))=0 \] is also oscillatory.
reviewed by: Zuzana Došlá
Mathematics Subject Classification ID: 34C10
zbMATH DE Number: 2137118
zbMATH Keywords: oscillation
zbMATH Keywords: nonoscillation
zbMATH Keywords: comparison
zbMATH Keywords: superlinear
zbMATH Keywords: linearization
MaRDI profile type: Publication
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full work available at URL: s0895-7177(04)90538-9
OpenAlex ID: W1998481752
description: scientific article; zbMATH DE number 2137118