Estimates for solutions to a class of nonautonomous systems of neutral type with unbounded delay
type: Item
instance of: scholarly article
title: Estimates for solutions to a class of nonautonomous systems of neutral type with unbounded delay
zbMATH Open document ID: 1484.34158
DOI: 10.1134/S0037446621030101
published in: Siberian Mathematical Journal
publication date: 2021-06-07T00:00:00Z
review text: The paper deals with nonlinear systems of nonautonomous differential equations of neutral type with unbounded delay of the form \[ \frac{d}{dt} y(t)= A(t)\,y(t)+ B(t)\, y(t-\tau(t))+C(t)\, \frac{d}{dt} y(t-\tau(t))\] \[\\ \quad + F\left(t,y(t),y(t-\tau(t)), \frac{d}{dt} y(t-\tau(t)\right)\,,\; t\geq 0\,.\] By means of appropriate Lyapunov-Krasovskii functionals, the author studies the stability of solutions, first for the linear case, and then for some nonlinear ones when \(\|F(t,u,v,w)\|\leq q\, \|u\|^{1+w}\) with \(w\geq 0\). In the particular case of exponential and asymptotic stability, some estimates about the attraction domain are obtained.
reviewed by: Sylvia Novo
Mathematics Subject Classification ID: 34K20
Mathematics Subject Classification ID: 34K40
Mathematics Subject Classification ID: 34K25
Mathematics Subject Classification ID: 37C60
zbMATH DE Number: 7356189
zbMATH Keywords: differential equation of neutral type
zbMATH Keywords: variable coefficients
zbMATH Keywords: estimates for solutions
zbMATH Keywords: stability
zbMATH Keywords: Lyapunov-Krasovskii functional
author: I. I. Matveeva
MaRDI profile type: Publication
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full work available at URL: s0037446621030101
OpenAlex ID: W3168644739
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description: scientific article; zbMATH DE number 7356189