Oscillation theorems of higher-order nonlinear delay differential equations
type: Item
instance of: scholarly article
title: Oscillation theorems of higher-order nonlinear delay differential equations
zbMATH Open document ID: 0880.34073
DOI: 10.1007/BF02451636
author: Mingzhong Jin
published in: Applied Mathematics and Mechanics. (English Edition)
publication date: 1995-02-23T00:00:00Z
review text: Necessary and sufficient conditions for oscillation of a class of higher-order nonlinear delay differential equations of the form: \[ [a(t)x^{(2n-1)}(t)]'+ b(t)\phi[x(t)]p(x'(t))+ \sum q_i(t)g_i[x'(t-\sigma_i(t))] f_i[x(t-\sigma_i(t))]= e(t), \] are given, where \(a\), \(b\), \(q_i\), \(\sigma_i\) \((1\leq i\leq m): I\to\mathbb{R}^+_0= [0,\infty)\), \(I= [t_0,\infty)\); \(p\), \(f_i\) \((1\leq i\leq m)\): \(\mathbb{R}\to\mathbb{R}\); \(\phi\), \(g_i\) \((1\leq i\leq m)\): \(\mathbb{R}\to\mathbb{R}^+\); \(e:I\to\mathbb{R}\). All the functions are continuous and \(xf_i(x)>0\) for \(x\neq 0\) and \(yp(y)>0\) for \(y\neq 0\). Some sufficient conditions and necessary conditions for oscillation of a forced delay differential equation are also given.
Mathematics Subject Classification ID: 34K20
Mathematics Subject Classification ID: 34C15
zbMATH DE Number: 707466
zbMATH Keywords: oscillation
zbMATH Keywords: higher-order nonlinear delay differential equations
reviewed by: Olusola Akinyele
MaRDI profile type: Publication
cites work: Oscillation theorems of nth-order functional differential equations with forcing terms
cites work: Nonoscillatory solutions of higher order delay equations
cites work: Oscillation theorems for nth-order delay differential equations
cites work: Asymptotic and oscillatory behavior of \(n\)th order forced functional differential equations
cites work: Asymptotically Periodic Solutions of a Class of Second Order Nonlinear Differential Equations
cites work: Second Order Nonlinear Forced Oscillations
full work available at URL: https://doi.org/10.1007/bf02451636
OpenAlex ID: W2006590549
description: scientific article; zbMATH DE number 707466