Oscillation criteria for a class of second-order Emden-Fowler delay dynamic equations on time scales
type: Item
instance of: scholarly article
title: Oscillation criteria for a class of second-order Emden-Fowler delay dynamic equations on time scales
zbMATH Open document ID: 1125.34047
author: Zhenlai Han
author: Shurong Sun
author: Bao Shi
published in: Journal of Mathematical Analysis and Applications
publication date: 2007-07-19T00:00:00Z
review text: The authors establish several new oscillation criteria for second order dynamic equations \[ x^{\Delta\Delta}(t)+p(t)\,x^\gamma(\tau(t))=0 \] of Emden-Fowler type on an unbounded time scale \({\mathbb T}\) (which is by definition any nonempty closed subset of \({\mathbb R}\)). The exponent \(\gamma\) is a quotient of odd positive integers, \(p(\cdot)\) is positive and rd-continuous, and \(\tau:{\mathbb T}\to{\mathbb T}\) is rd-continuous, sublinear, i.e., \(\tau(t)\leq t\), and \(\tau(t)\to\infty\) as \(t\to\infty\). The main tool in deriving these oscillation criteria is a Riccati technique and, in some cases, the Keller--Pötzsche time scale chain rule.
reviewed by: Roman Šimon Hilscher
Mathematics Subject Classification ID: 34K11
Mathematics Subject Classification ID: 39A10
Mathematics Subject Classification ID: 39A13
zbMATH DE Number: 5172990
zbMATH Keywords: Time scale
zbMATH Keywords: Delay dynamic equation
zbMATH Keywords: Oscillation
MaRDI profile type: Publication
full work available at URL: j.jmaa.2007.01.004
OpenAlex ID: W1983866211
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DOI: 10.1016/J.JMAA.2007.01.004
description: scientific article; zbMATH DE number 5172990