Interval criteria for oscillation of second-order half-linear differential equations.
type: Item
instance of: scholarly article
title: Interval criteria for oscillation of second-order half-linear differential equations.
zbMATH Open document ID: 1053.34034
published in: Journal of Mathematical Analysis and Applications
publication date: 2004-03-14T00:00:00Z
review text: The authors consider the second-order half-linear differential equation \[ [r(t)| x'|^{\alpha- 1} x']'+ q(t)| x|^{\alpha-1} x=0 \] with \(\alpha> 0\). By employing the techniques used by Q. Kong for the linear case, they establish interval criteria for oscillation, i.e., criteria for oscillation based on the information of the equation on a sequence on intervals rather than on the half-line \([0,\infty)\). Several follow-up sufficient conditions are obtained. A couple of examples are also given for demonstration. Here, it should be pointed out that due to lack of research sources, the authors did not know that similar work has been done by \textit{Q. Kong} [Fields Inst. Commun. 21, 317--323 (1999; Zbl 0924.34025)]. The present work should be regarded as a generalization of the above Kong's work using a more general Riccati variable.
Mathematics Subject Classification ID: 34C10
zbMATH DE Number: 2056507
zbMATH Keywords: half-linear differential equation
zbMATH Keywords: interval criteria
zbMATH Keywords: oscillation
zbMATH Keywords: generalized Riccati technique
zbMATH Keywords: integral averaging method
author: Qiru Wang
author: Qi-Gui Yang
reviewed by: Qingkai Kong
MaRDI profile type: Publication
full work available at URL: j.jmaa.2003.10.028
OpenAlex ID: W2092861553
cites work: Q4750126
cites work: An Oscillation Criterion for a Forced Second-Order Linear Differential Equation
cites work: Q4039929
cites work: Oscillation and nonoscillation of second order linear differential equations
cites work: Q4167008
cites work: Interval criteria for oscillation of second-order linear ordinary differential equations
cites work: Integral inequalities and second order linear oscillation
cites work: Oscillation criteria for second order linear differential equations
cites work: Sturmian comparison theorem for half-linear second-order differential equations
cites work: Interval oscillation criteria for second-order nonlinear differential equations with damping
cites work: Interval oscillation criteria related to integral averaging technique for certain nonlinear differential equations
cites work: An oscillation criterion for nonhomogeneous half-linear differential equations
cites work: Oscillation criteria for second-order half-linear differential equations.
cites work: Oscillation theorems for linear differential equations of second order
cites work: Oscillation and asymptotics for second-order half-linear differential equations
DOI: 10.1016/J.JMAA.2003.10.028
description: scientific article; zbMATH DE number 2056507