Oscillations of functional differential equations generated by advanced arguments
type: Item
instance of: scholarly article
title: Oscillations of functional differential equations generated by advanced arguments
zbMATH Open document ID: 0732.34057
published in: Differential and Integral Equations
publication date: 1989-01-01T00:00:00Z
review text: We consider the functional differential equation \((1)\quad L_ nx(t)+\delta f(t,x[g_ 1(t)],...,x[g_ m(t)])=0,\) where \(n\geq 2\), \(\delta =\pm 1\), \(L_ 0x(t)=x(t)\), \(L_ kx(t)=(1/a_ k(t))(L_{k- 1}x(t))d/dt\), \(k=1,2,...,n\), \(a_ n=1\), \(a_ i: {\mathbb{R}}_+\to {\mathbb{R}}_+\setminus \{0\}\), \(i=1,2,...,n-1\), \(g_ i: {\mathbb{R}}_+\to {\mathbb{R}}_+=[0,\infty)\), \(i=1,2,...,m\), f: \({\mathbb{R}}_+\times {\mathbb{R}}^ m\to {\mathbb{R}}=(-\infty,\infty)\) are continuous and \(g_ i(t)\geq t\) on \({\mathbb{R}}_+\) for \(i=1,2,...,m\). We always assume \(\int^{\infty}a_ i(s)ds=\infty,\quad i=1,2,...,n-1.\) The main purpose of this paper is to establish some criteria for equation (1) to be oscillatory or almost oscillatory. The behavioural properties obtained for equation (1) are generated by the advanced arguments \(g_ i (i=1,2,...,m)\) and are not valid for the corresponding ordinary differential equations.
Mathematics Subject Classification ID: 34K99
Mathematics Subject Classification ID: 34C10
zbMATH DE Number: 4210605
zbMATH Keywords: functional differential equation
zbMATH Keywords: oscillatory
zbMATH Keywords: almost oscillatory
zbMATH Keywords: advanced arguments
author: Said R. Grace
author: Bikkar S. Lalli
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4210605