Sharp estimation for the solutions of inhomogeneous delay differential and Halanay-type inequalities

István Győri, László Horváth

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

This paper is devoted to inhomogeneous Halanay-type inequalities together with inhomogeneous linear delay differential inequalities and equations. Based on the the variation of constants formula and some results borrowed from a recent paper of the authors, sharp conditions for the boundedness and the existence of the limit of the nonnegative solutions are established. The sharpness of the results are illustrated by examples and by comparison of results in some earlier works.

Original languageEnglish
Article number54
JournalElectronic Journal of Qualitative Theory of Differential Equations
Volume2018
DOIs
Publication statusPublished - Jan 1 2018

Fingerprint

Variation of Constants Formula
Delay Equations
Nonnegative Solution
Sharpness
Differential Inequalities
Boundedness
Differential equation

Keywords

  • Delay differential equation
  • Delay differential inequality
  • Halanay inequality

ASJC Scopus subject areas

  • Applied Mathematics

Cite this

@article{7e6bec8748e84b2a8cfea512e93450ec,
title = "Sharp estimation for the solutions of inhomogeneous delay differential and Halanay-type inequalities",
abstract = "This paper is devoted to inhomogeneous Halanay-type inequalities together with inhomogeneous linear delay differential inequalities and equations. Based on the the variation of constants formula and some results borrowed from a recent paper of the authors, sharp conditions for the boundedness and the existence of the limit of the nonnegative solutions are established. The sharpness of the results are illustrated by examples and by comparison of results in some earlier works.",
keywords = "Delay differential equation, Delay differential inequality, Halanay inequality",
author = "Istv{\'a}n Győri and L{\'a}szl{\'o} Horv{\'a}th",
year = "2018",
month = "1",
day = "1",
doi = "10.14232/ejqtde.2018.1.54",
language = "English",
volume = "2018",
journal = "Electronic Journal of Qualitative Theory of Differential Equations",
issn = "1417-3875",
publisher = "University of Szeged",

}

TY - JOUR

T1 - Sharp estimation for the solutions of inhomogeneous delay differential and Halanay-type inequalities

AU - Győri, István

AU - Horváth, László

PY - 2018/1/1

Y1 - 2018/1/1

N2 - This paper is devoted to inhomogeneous Halanay-type inequalities together with inhomogeneous linear delay differential inequalities and equations. Based on the the variation of constants formula and some results borrowed from a recent paper of the authors, sharp conditions for the boundedness and the existence of the limit of the nonnegative solutions are established. The sharpness of the results are illustrated by examples and by comparison of results in some earlier works.

AB - This paper is devoted to inhomogeneous Halanay-type inequalities together with inhomogeneous linear delay differential inequalities and equations. Based on the the variation of constants formula and some results borrowed from a recent paper of the authors, sharp conditions for the boundedness and the existence of the limit of the nonnegative solutions are established. The sharpness of the results are illustrated by examples and by comparison of results in some earlier works.

KW - Delay differential equation

KW - Delay differential inequality

KW - Halanay inequality

UR - http://www.scopus.com/inward/record.url?scp=85050159385&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85050159385&partnerID=8YFLogxK

U2 - 10.14232/ejqtde.2018.1.54

DO - 10.14232/ejqtde.2018.1.54

M3 - Article

AN - SCOPUS:85050159385

VL - 2018

JO - Electronic Journal of Qualitative Theory of Differential Equations

JF - Electronic Journal of Qualitative Theory of Differential Equations

SN - 1417-3875

M1 - 54

ER -