Oscillation criteria for nonlinear differential equations with damping.
type: Item
instance of: scholarly article
title: Oscillation criteria for nonlinear differential equations with damping.
zbMATH Open document ID: 1034.34041
DOI: 10.1016/S0096-3003(02)00079-6
author: Xiaojing Yang
published in: Applied Mathematics and Computation
publication date: 2003-01-28T00:00:00Z
review text: The author presents oscillation criteria for the damped nonlinear differential equation \[ (r(t)x')'+ p(t)x' + q(t)f(x)=0, \tag{*} \] where \(r,f\) are continuously differentiable functions, \(r(t)>0\), \(p,q\) are continuous, \(xf(x)>0\) for \(x\neq 0\), and it is supposed that there exists \(\lambda>0\) such that \(f'(x)>\lambda\) for \(x\in \mathbb{R}\). Under the last assumption on the derivative \(f'\), equation (*) is, in a certain sense, the Sturmian majorant of the linear equation \[ (r(t)y')'+p(t)y+ \lambda q(t)y=0. \tag{**} \] Using a combination of the generalized Riccati substitution and the \(H\)-function averaging technique, conditions on the functions \(r,p,q\) are given which guarantee that (**) is oscillatory and this, in turn, implies that (*) possesses no nonoscillatory solution which is extensible up to \(\infty\). The obtained oscillation criteria are illustrated by a number of examples and corollaries.
Mathematics Subject Classification ID: 34C10
zbMATH DE Number: 1861410
zbMATH Keywords: Damping
zbMATH Keywords: Oscillation criteria
zbMATH Keywords: Nonlinear differential equations.
reviewed by: Ondřej Došlý
MaRDI profile type: Publication
cites work: A criterion of oscillatory stability
cites work: On Non-Oscillatory Linear Differential Equations of Second Order
cites work: Q4167008
cites work: Interval criteria for oscillation of second-order linear ordinary differential equations
cites work: Oscillation criteria for second order linear differential equations
cites work: Oscillation theorems for linear differential equations of second order
cites work: Interval oscillation criteria for second-order nonlinear differential equations with damping
cites work: Q5330830
full work available at URL: s0096-3003(02)00079-6
OpenAlex ID: W2030155469
description: scientific article; zbMATH DE number 1861410