Oscillations of half-linear second order differential equations
type: Item
instance of: scholarly article
title: Oscillations of half-linear second order differential equations
zbMATH Open document ID: 0872.34019
author: Horng-Jaan Li
author: Cheh-Chih Yeh
published in: Hiroshima Mathematical Journal
publication date: 1997-10-20T00:00:00Z
review text: Let \(\varphi:\mathbb{R}\to\mathbb{R}\) be defined by \(\varphi(s)=|s|^{p-2}s\), with \(p>1\) a fixed number. We extend Sturm's comparison theorem of the linear differential equation \[ {\textstyle {\frac{d}{dt}}} [r(t)u'(t)]+ c(t)u(t)=0 \] to the nonlinear differential equation \[ {\textstyle {\frac{d}{dt}}} \{r(t)\varphi(u'(t))\}+ c(t)\varphi(u(t))=0, \tag{E} \] by using the Wirtinger inequality. A Lyapunov inequality and some oscillation criteria of (E) are also given.
reviewed by: J.Vosmanský
Mathematics Subject Classification ID: 34C10
Mathematics Subject Classification ID: 34C15
zbMATH DE Number: 863653
zbMATH Keywords: Riccati equation
zbMATH Keywords: Willet's oscillation criterion
zbMATH Keywords: Sturm comparison theorem
zbMATH Keywords: Wirtinger inequality
zbMATH Keywords: Lyapunov inequality
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 863653