Oscillation theorems for nonlinear second-order differential equations
type: Item
instance of: scholarly article
title: Oscillation theorems for nonlinear second-order differential equations
zbMATH Open document ID: 1059.34023
DOI: 10.1016/S0898-1221(02)00167-0
author: B. Ayanlara
author: Aydin Tiryaki
publication date: 2004-11-18T00:00:00Z
review text: The authors study the second-order nonlinear differential equation \[ [r(t)\Phi(x(t))\varphi\bigl(x'(t)\bigr)]' +c(t)\varphi(x(t))=0\tag{1} \] on the interval \([t_0,\infty)\). The functions \(r:[t_0,\infty)\to(0,\infty)\), \(c:[t_0,\infty)\to \mathbb{R}\) and \(\Phi:\mathbb{R}\to(0,\gamma]\) are supposed to be continuous, \(\gamma\) is a real number. The function \(\varphi\) is defined as a generalized power function \(\varphi(x)=| x| ^{p-2}x\) for fixed real \(p>1\). The authors study the proper solutions of equation (1) and by using the Riccati-type transformation and integral averaging technique with the averaging \(H\)-function (originally due to \textit{Ch. G. Philos} [Arch. Math. 53, 482--492 (1989; Zbl 0661.34030)]), they prove integral oscillation criteria for equation (1).
reviewed by: Robert Mařík
Mathematics Subject Classification ID: 34C10
zbMATH DE Number: 2116486
zbMATH Keywords: oscillation
zbMATH Keywords: Riccati substitution
zbMATH Keywords: second order
zbMATH Keywords: nonlinear differential equation
zbMATH Keywords: integral averages
MaRDI profile type: Publication
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published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 2116486