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 $\dot x(t) =-c(t)x(t-\tau(t))$

Type

journal article in Web of Science

Language

English

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.

Keywords

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

Authors

DIBLÍK, J.

RIV year

2015

Released

6. 6. 2015

Publisher

Elsevier

ISBN

0001-8708

Periodical

ADVANCES IN MATHEMATICS

Year of study

280

Number

1

State

United States of America

Pages from

1

Pages to

20

Pages count

20

URL

https://www.sciencedirect.com/science/article/pii/S000187081500136X

BibTex

@article{BUT115049,
  author="Josef {Diblík}",
  title="Explicit integral criteria for the existence of positive solutions of the linear delayed equation $\dot x(t) =-c(t)x(t-\tau(t))$",
  journal="ADVANCES IN MATHEMATICS",
  year="2015",
  volume="280",
  number="1",
  pages="1--20",
  doi="10.1016/j.aim.2015.04.013",
  issn="0001-8708",
  url="https://www.sciencedirect.com/science/article/pii/S000187081500136X"
}