Publication detail

# New explicit integral criteria for the existence of positive solutions to the linear advanced equation $\dot x(t) = c (t) x (t + \tau)$

DIBLÍK, J. KÚDELČÍKOVÁ, M.

Original Title

New explicit integral criteria for the existence of positive solutions to the linear advanced equation $\dot x(t) = c (t) x (t + \tau)$

English Title

New explicit integral criteria for the existence of positive solutions to the linear advanced equation $\dot x(t) = c (t) x (t + \tau)$

Type

journal article in Web of Science

Language

en

Original Abstract

The paper is devoted to the investigation of a linear differential equation with advanced argument $y'(t)=c(t)y(t+\tau)$ where $\tau>0$ is a constant advanced argument and the function $c\colon [t_0,\infty)\to [0,\infty)$, $t_0\in \bR$ is bounded and locally Lipschitz continuous. New explicit integral criteria for the existence of a positive solution in terms of $c$ and $\tau$ are derived and their efficiency is demonstrated.

English abstract

The paper is devoted to the investigation of a linear differential equation with advanced argument $y'(t)=c(t)y(t+\tau)$ where $\tau>0$ is a constant advanced argument and the function $c\colon [t_0,\infty)\to [0,\infty)$, $t_0\in \bR$ is bounded and locally Lipschitz continuous. New explicit integral criteria for the existence of a positive solution in terms of $c$ and $\tau$ are derived and their efficiency is demonstrated.

Keywords

advanced linear differential equation, positive solution, explicit criterion

RIV year

2014

Released

02.12.2014

Publisher

PERGAMON-ELSEVIER SCIENCE LTD

Location

THE BOULEVARD, LANGFORD LANE, KIDLINGTON, OXFORD OX5 1GB, ENGLAND

ISBN

0893-9659

Periodical

APPLIED MATHEMATICS LETTERS

Year of study

38

Number

2014

State

US

Pages from

144

Pages to

148

Pages count

5

URL

Documents

BibTex

```
@article{BUT110580,
author="Josef {Diblík} and Mária {Kúdelčíková}",
title="New explicit integral criteria for the existence of positive solutions to the linear advanced equation $\dot x(t) = c (t) x (t + \tau)$",
annote="The paper is devoted to the investigation of a linear differential equation with advanced argument $y'(t)=c(t)y(t+\tau)$ where $\tau>0$ is a constant advanced argument
and the function $c\colon [t_0,\infty)\to [0,\infty)$, $t_0\in \bR$ is bounded and locally Lipschitz continuous. New explicit integral criteria for the existence of a positive solution in terms of $c$ and $\tau$ are derived and their efficiency is demonstrated.",
address="PERGAMON-ELSEVIER SCIENCE LTD",
chapter="110580",
doi="10.1016/j.aml.2014.06.020",
howpublished="online",
institution="PERGAMON-ELSEVIER SCIENCE LTD",
number="2014",
volume="38",
year="2014",
month="december",
pages="144--148",
publisher="PERGAMON-ELSEVIER SCIENCE LTD",
type="journal article in Web of Science"
}
```