Properties of Kneser's solution for half-linear third order neutral differential equations
type: Item
instance of: scholarly article
title: Properties of Kneser's solution for half-linear third order neutral differential equations
zbMATH Open document ID: 1399.34186
published in: Acta Mathematica Hungarica
publication date: 2018-02-13T00:00:00Z
review text: The authors consider the third-order neutral differential equation of advanced type \[ (a(t)(b(t)(z'(t))^\alpha)')'+q(t)y^\alpha(t)=0, \] where \(\alpha\) is a ratio of odd positive integers, \(z(t)=y(t)+p(t)y(\sigma(t))\), \(\sigma(t)\geq t\), \(a,b,\sigma,q\) are continuous and positive functions, and some other hypotheses are assumed. Sufficient conditions are established which guarantee that all nonoscillatory solutions of this equation are of Kneser type, i.e., \(y(t)>0,y'(t)<0,((y'(t))^\alpha),((y'(t))^\alpha)''<0\) for large \(t\). In addition, estimates for these solutions are derived.
reviewed by: Pavel Rehak
Mathematics Subject Classification ID: 34K11
Mathematics Subject Classification ID: 34K12
Mathematics Subject Classification ID: 34K40
zbMATH DE Number: 6837896
zbMATH Keywords: third-order differential equation
zbMATH Keywords: Kneser's solution
zbMATH Keywords: oscillation
author: B. Baculíková
author: Bose Rani
author: S. Selvarangam
author: E. Thandapani
MaRDI profile type: Publication
full work available at URL: s10474-017-0721-7
OpenAlex ID: W2614881550
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DOI: 10.1007/S10474-017-0721-7
description: scientific article; zbMATH DE number 6837896