Oscillation theorems for second-order equations with damping
type: Item
instance of: scholarly article
title: Oscillation theorems for second-order equations with damping
zbMATH Open document ID: 0972.34022
DOI: 10.1016/S0362-546X(98)00324-1
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2001-11-04T00:00:00Z
review text: Here, the oscillation of the nonlinear second-order differential equation with damping \[ [r(t)x'(t)]'+p(t)x'(t)+q(t)f(x(t))=0, \tag{1} \] with \(r\in C^1([t_0,\infty);(0,\infty))\),\ \(p,q\in C([t_0,\infty);(-\infty,\infty))\), \(f\in C((-\infty,\infty);(-\infty,\infty))\) and \(xf(x)>0\) for \(x\neq 0\) is investigated. Some new oscillation criteria are given. They generalize several earlier oscillation results of similar type and can be applied in some cases in which other known oscillation theorems are not applicable. Also a theorem on the asymptotic behavior of solutions to the forced equation \([r(t)x'(t)]'+p(t)x'(t)+q(t)f(x(t))=e(t)\) is presented.
reviewed by: Jan Ohriska
Mathematics Subject Classification ID: 34C10
zbMATH DE Number: 1526191
zbMATH Keywords: oscillation theory
author: Yuriy V. Rogovchenko
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1526191