Publication detail

# A note on explicit criteria for the existence of positive solutions to the linear advanced equation \dot (t) = c(t)x(t + \tau).

DIBLÍK, J.

Original Title

A note on explicit criteria for the existence of positive solutions to the linear advanced equation \dot (t) = c(t)x(t + \tau).

English Title

A note on explicit criteria for the existence of positive solutions to the linear advanced equation \dot (t) = c(t)x(t + \tau).

Type

journal article in Web of Science

Language

en

Original Abstract

The paper investigates a linear differential equation with advanced argument \dot (t) = c(t)x(t + \tau), where \tau > 0 and the function c: [t_0,\infty) \to (0,\infty), t_0 \in R is bounded and locally Lipschitz continuous. New explicit criteria for the existence of a positive solution in terms of c and \tau are derived. An overview of known relevant criteria is provided and relevant comparisons are also given.

English abstract

The paper investigates a linear differential equation with advanced argument \dot (t) = c(t)x(t + \tau), where \tau > 0 and the function c: [t_0,\infty) \to (0,\infty), t_0 \in R is bounded and locally Lipschitz continuous. New explicit criteria for the existence of a positive solution in terms of c and \tau are derived. An overview of known relevant criteria is provided and relevant comparisons are also given.

Keywords

advanced argument, linear differential equation, positive solution, explicit criterion

RIV year

2014

Released

03.11.2014

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

35

Number

2014

State

US

Pages from

72

Pages to

76

Pages count

5

URL

Documents

BibTex

```
@article{BUT111847,
author="Josef {Diblík}",
title="A note on explicit criteria for the existence of positive solutions to the linear advanced equation \dot (t) = c(t)x(t + \tau).",
annote="The paper investigates a linear differential equation with advanced argument \dot (t) = c(t)x(t + \tau), where \tau > 0 and the function c: [t_0,\infty) \to (0,\infty), t_0 \in R is bounded and locally Lipschitz continuous. New explicit criteria for the existence of a positive solution in terms of c and \tau are derived. An overview of known relevant criteria is provided and relevant comparisons are also given.",
address="PERGAMON-ELSEVIER SCIENCE LTD",
chapter="111847",
doi="10.1016/j.aml.2013.11.010",
howpublished="online",
institution="PERGAMON-ELSEVIER SCIENCE LTD",
number="2014",
volume="35",
year="2014",
month="november",
pages="72--76",
publisher="PERGAMON-ELSEVIER SCIENCE LTD",
type="journal article in Web of Science"
}
```