Oscillation criteria for second order linear differential equations
type: Item
instance of: scholarly article
title: Oscillation criteria for second order linear differential equations
zbMATH Open document ID: 0836.34033
author: Horng-Jaan Li
published in: Journal of Mathematical Analysis and Applications
publication date: 1996-04-22T00:00:00Z
review text: It is considered the differential equation (1) \(|r(t)x']' + c(t)x = 0\), where \(r \in C^1 ([t_0, \infty)\); \((0, \infty))\), \(c \in C ([t_0, \infty); \mathbb{R})\) and \(t_0 \geq 0\). The author gives new oscillation criteria for (1) which improve results of A. Wintner, P. Hartman, I. V. Kamenev, J. Yan and Ch. G. Philos. The criteria are proved by using a generalized Riccati transformation due to \textit{Y. H. Yu} [Math. Nachr. 153, 137-143 (1991; Zbl 0795.34025)] of the form \[ v(t) = \exp \Bigl( - 2 \int^t f(s)ds \Bigr) r(t) \left( {x'(t) \over x(t)} + f(t) \right), \] where \(f \in C^1 ([t_0, \infty); \mathbb{R})\) is a given function.
Mathematics Subject Classification ID: 34C10
Mathematics Subject Classification ID: 34A30
zbMATH DE Number: 811231
zbMATH Keywords: oscillation criteria
zbMATH Keywords: generalized Riccati transformation
reviewed by: Svatoslav Staněk
MaRDI profile type: Publication
full work available at URL: jmaa.1995.1295
OpenAlex ID: W1986780760
DOI: 10.1006/JMAA.1995.1295
description: scientific article; zbMATH DE number 811231