Qualitative analysis of positive solutions of first-order functional differential equations of neutral type
type: Item
instance of: scholarly article
title: Qualitative analysis of positive solutions of first-order functional differential equations of neutral type
zbMATH Open document ID: 0980.34075
DOI: 10.1016/S0362-546X(98)00254-5
author: Horng-Jaan Li
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2002-02-22T00:00:00Z
review text: The paper is concerned with the asymptotic behavior of solutions to the first-order neutral differential equation (1) \([x(t)-x(t-\tau)]'+F(t,x(g(t)))=0\) for \(t\geq t_0\geq 0\), where \(\tau\) is a positive constant; \(F(t,x)\in C([t_0,\infty)\times\mathbb R,\mathbb R)\), \(\text{sgn}F(t,x)=\text{sgn}x\), \(F(t,x)\) is nondecreasing in \(x\); \(g(t)\in C([t_0,\infty),\mathbb R)\), \(g(t)\leq t\) for \(t\geq t_0\), \(\lim_{t\to\infty}g(t)=\infty\). A classification of all positive solutions to equation (1) is given and some results known for the equation \([x(t)-x(t-\tau)]'+p(t)x(t-\sigma)=0\) are extended to equation (1). Moreover, some comparison results are derived.
Mathematics Subject Classification ID: 34K25
Mathematics Subject Classification ID: 34K40
zbMATH DE Number: 1419535
zbMATH Keywords: asymptotic theory
zbMATH Keywords: neutral equations
reviewed by: Jan Ohriska
MaRDI profile type: Publication
full work available at URL: s0362-546x(98)00254-5
OpenAlex ID: W2034046524
description: scientific article; zbMATH DE number 1419535