Publication detail

# Explicit integral criteria for the existence of positive solutions of the linear delayed equation $\dot x(t) =-c(t)x(t-\tau(t))$

DIBLÍK, J.

Original Title

Explicit integral criteria for the existence of positive solutions of the linear delayed equation $\dot x(t) =-c(t)x(t-\tau(t))$

English Title

Explicit integral criteria for the existence of positive solutions of the linear delayed equation $\dot x(t) =-c(t)x(t-\tau(t))$

Type

journal article in Web of Science

Language

en

Original Abstract

The paper analyses the linear differential equation with single delay $\dot x(t)=-c(t)x(t-\tau(t))$ with continuous $\tau\colon [t_0,\infty)\to (0,r]$, $r>0$, $t_0\in \bR$, and $c\colon [t_0-r,\infty)\to (0,\infty)$. New explicit integral criteria for the existence of a positive solution expressed in terms of $c$ and $\tau$ are derived, an overview of known relevant criteria is provided, and relevant comparisons are also given. It is demonstrated that the known criteria are consequences of the new results.

English abstract

The paper analyses the linear differential equation with single delay $\dot x(t)=-c(t)x(t-\tau(t))$ with continuous $\tau\colon [t_0,\infty)\to (0,r]$, $r>0$, $t_0\in \bR$, and $c\colon [t_0-r,\infty)\to (0,\infty)$. New explicit integral criteria for the existence of a positive solution expressed in terms of $c$ and $\tau$ are derived, an overview of known relevant criteria is provided, and relevant comparisons are also given. It is demonstrated that the known criteria are consequences of the new results.

Keywords

time delay, linear differential equation, positive solution, integral criterion

RIV year

2015

Released

06.06.2015

Publisher

Elsevier

ISBN

0001-8708

Periodical

ADVANCES IN MATHEMATICS

Year of study

280

Number

1

State

US

Pages from

1

Pages to

20

Pages count

20

URL

Documents

BibTex

```
@article{BUT115049,
author="Josef {Diblík}",
title="Explicit integral criteria for the existence of positive solutions of the linear delayed equation $\dot x(t) =-c(t)x(t-\tau(t))$",
annote="The paper analyses the linear differential equation with single delay $\dot x(t)=-c(t)x(t-\tau(t))$ with continuous $\tau\colon [t_0,\infty)\to (0,r]$, $r>0$, $t_0\in \bR$, and $c\colon [t_0-r,\infty)\to (0,\infty)$. New explicit integral criteria for the existence of a positive solution expressed in terms of $c$ and $\tau$ are derived, an overview of known relevant criteria is provided, and relevant comparisons are also given. It is demonstrated that the known criteria are consequences of the new results.",
address="Elsevier",
chapter="115049",
doi="10.1016/j.aim.2015.04.013",
howpublished="online",
institution="Elsevier",
number="1",
volume="280",
year="2015",
month="june",
pages="1--20",
publisher="Elsevier",
type="journal article in Web of Science"
}
```