Classifications and existence of positive solutions of higher order nonlinear iterative functional differential equations
type: Item
instance of: scholarly article
title: Classifications and existence of positive solutions of higher order nonlinear iterative functional differential equations
zbMATH Open document ID: 1004.34063
DOI: 10.1016/S0377-0427(01)00414-9
author: Shi Nian Zhang
author: Wan-Tong Li
published in: Journal of Computational and Applied Mathematics
publication date: 2002-05-21T00:00:00Z
review text: The authors consider a class of higher-order nonlinear iterative functional-differential equations of the form \[ (r(t) x^{(m- 1)}(t))'+ f(t, x(t), x(\Delta(t, x(t))))= 0\tag{1} \] in the case when \(\int^\infty ds/r(s)= \infty\). It should be noted that the deviating arguments depend on both the state variable \(x\) and the time \(t\) while in most of the papers the deviating arguments depend only on time. The authors investigate the asymptotic behaviour of the nonoscillatory solutions to (1). More precisely, they give a classification scheme of the eventually positive solutions according to their asymptotic behaviour as \(t\to\infty\). Further, they obtain necessary or sufficient conditions (or both in some cases) for the existence of solutions to (1) of any of the types introduced in their classification scheme.
Mathematics Subject Classification ID: 34K12
Mathematics Subject Classification ID: 34K25
zbMATH DE Number: 1743077
zbMATH Keywords: functional-differential equation
zbMATH Keywords: iterative asymptotic behaviour
zbMATH Keywords: positive solutions
reviewed by: V. Petrov
MaRDI profile type: Publication
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full work available at URL: s0377-0427(01)00414-9
OpenAlex ID: W1982366361
description: scientific article; zbMATH DE number 1743077