On oscillation of nonlinear second order differential equation with damping term
type: Item
instance of: scholarly article
title: On oscillation of nonlinear second order differential equation with damping term
zbMATH Open document ID: 1056.34052
DOI: 10.1007/BF02936088
author: Meili Li
author: Jurang Yan
author: Mian-sen Wang
published in: Journal of Applied Mathematics and Computing
publication date: 2004-05-18T00:00:00Z
review text: The authors study the second-order damped differential equation \[ [r(t)x'(t)]'+p(t)x'(t)+q(t)f(x(t))=0, \quad t\geq t_0, \] where \(r\in C^1([t_0,\infty))\), \(p,q\in C([t_0,\infty))\), \(f\in C((-\infty,\infty))\), \(r\) is a positive function and \(q\) is not identical to zero on any interval \([T,\infty)\) for \(T\) arbitrary large. The function \(f\) is supposed to satisfy the condition \(f(x)/x\geq K>0\) for some positive constant \(K\) and \(x\neq 0\). The authors present several new sufficient conditions which ensure that every continuable proper solution of the equation is oscillatory. The main idea of the proofs is the application of integral averaging technique and the two-parametric function \(H(t,s)\), originally due to \textit{Ch. G. Philos} [Arch. Math. 53, 482-492 (1989; Zbl 0661.34030)] and used extensively in the oscillation theory.
reviewed by: Robert Mařík
Mathematics Subject Classification ID: 34C10
Mathematics Subject Classification ID: 34C29
zbMATH DE Number: 2064706
zbMATH Keywords: oscillation
zbMATH Keywords: integral averages
zbMATH Keywords: oscillatory solution
zbMATH Keywords: damped equation
zbMATH Keywords: superlinear equation
Wikidata QID: Q115391066
MaRDI profile type: Publication
cites work: On oscillation of nonlinear second order differential equation with damping term.
cites work: On the oscillation of solutions of linear differential equations
cites work: On Non-Oscillatory Linear Differential Equations of Second Order
cites work: A criterion of oscillatory stability
cites work: A Note on an Oscillation Criterion for an Equation with Damped Term
cites work: Oscillation Theorems for Second Order Linear Differential Equations with Damping
cites work: Oscillation Theorems for Nonlinear Second Order Differential Equations with Damped Term
cites work: Oscillation theorems for nonlinear differential equations of second order
cites work: Oscillation theorems for linear differential equations of second order
cites work: Oscillation criteria for certain nonlinear differential equations
cites work: Q4778342
cites work: Oscillation and stability of nonlinear neutral impulsive delay differential equations
cites work: Q4519034
full work available at URL: https://doi.org/10.1007/bf02936088
OpenAlex ID: W2036234246
description: scientific article; zbMATH DE number 2064706