Oscillation and asymptotic behaviour of a higher-order nonlinear neutral-type functional differential equation with oscillating coefficients
type: Item
instance of: scholarly article
title: Oscillation and asymptotic behaviour of a higher-order nonlinear neutral-type functional differential equation with oscillating coefficients
zbMATH Open document ID: 1222.34083
DOI: 10.1155/2011/158060
author: Mustafa Kemal Yildiz
author: Emrah Karaman
author: Hülya Durur
published in: Journal of Applied Mathematics
publication date: 2011-07-22T00:00:00Z
review text: Summary: We study the oscillation of bounded solutions of higher-order nonlinear neutral delay differential equations of the following type: \[ [y(t) + p(t)f(y(\tau(t)))]^{(n)} + q(t)h(y(\sigma(t))) = 0,\quad t \geq t_0,\quad t \in \mathbb R, \] where \(p \in C([t_0, \infty), \mathbb R)\), \(\lim_{t \rightarrow \infty}p(t) = 0\), \(q\in C([t_0, \infty)\), \(\mathbb R^+)\), \(\tau, \sigma\in C([t_0, \infty), \mathbb R)\), \(\tau(t), \sigma(t) < t\), \(\lim_{t \rightarrow \infty} \tau(t), \sigma(t) = \infty\), and \(f, h \in C(\mathbb R, \mathbb R)\). We obtain sufficient conditions for the oscillation of all solutions of this equation.
Mathematics Subject Classification ID: 34K11
Mathematics Subject Classification ID: 34K25
Mathematics Subject Classification ID: 34K40
zbMATH DE Number: 5930809
zbMATH Keywords: oscillation and asymptotic behaviour
zbMATH Keywords: higher-order nonlinear neutral-type functional differential equation
zbMATH Keywords: oscillating coefficients
Wikidata QID: Q58690269
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2011/158060
OpenAlex ID: W2090178888
cites work: Q4323870
cites work: Q4000352
cites work: Q5505200
cites work: Oscillatory behaviour of higher order neutral type nonlinear forced differential equations with oscillating coefficients.
cites work: Multiple solutions for a system of \((n_i p_i)\) boundary value problems
cites work: The oscillation of higher-order differential equations with deviating arguments
cites work: Q4244038
cites work: Oscillation theorems for nth-order delay differential equations
cites work: Oscillations of higher order differential equations of neutral type
cites work: Q4502956
cites work: Iterated oscillation criteria for delay dynamic equations of first order
cites work: Q4858386
cites work: Q3759218
cites work: Q4001772
cites work: Oscillation theorems for certain neutral differential equations
description: scientific article; zbMATH DE number 5930809