On oscillation and nonoscillation of general functional differential equations
type: Item
instance of: scholarly article
title: On oscillation and nonoscillation of general functional differential equations
zbMATH Open document ID: 0591.34056
DOI: 10.1016/0022-247X(85)90166-0
published in: Journal of Mathematical Analysis and Applications
publication date: 1985-01-01T00:00:00Z
review text: The n-th order functional differential equation (1) \(L_ nx(t)+f(t,x(t),x(g(t)))=h(t),\) where \(L_ 0x=x\), \(L_ kx=a_ k(L_{k- 1}x)'\), \(k=1,...,n\), \(a_ n=1\), is considered. Conditions which guarantee that any oscillatory solution of (1), satisfying a growth estimate, tends to 0 as \(t\to \infty\) (together with \(L_ kx\), \(k=1,...,n-1)\) are given. As consequences, some nonoscillation criteria for (1) are derived. Moreover, necessary and sufficient conditions so that all oscillatory solutions of \(L_ nx(t)+q(t)f(x(g(t)))=h(t)\) tend to 0 as \(t\to \infty\) are established.
Mathematics Subject Classification ID: 34K99
Mathematics Subject Classification ID: 34K25
zbMATH DE Number: 3948809
zbMATH Keywords: n-th order functional differential equation
zbMATH Keywords: oscillatory solution
zbMATH Keywords: growth estimate
zbMATH Keywords: nonoscillation criteria
author: Said R. Grace
author: Bikkar S. Lalli
MaRDI profile type: Publication
cites work: On the nonoscillation of perturbed functional differential equations
cites work: Asymptotic Decay of Oscillatory Solutions of Second Order Differential Equations with Forcing Term
cites work: A nonoscillation theorem for a second order sublinear retarded differential equation
cites work: Necessary and sufficient condition for eventual decay of oscillations in general functional equations with delays
cites work: A correction to ''forced oscillations in general ordinary differential equations with deviating arguments''
full work available at URL: 0022-247x(85)90166-0
OpenAlex ID: W2021670143
description: scientific article; zbMATH DE number 3948809