Publication detail

Integral criteria for the existence of positive solutions of first-order linear differential advanced-argument equations

DIBLÍK, J.

Original Title

Integral criteria for the existence of positive solutions of first-order linear differential advanced-argument equations

English Title

Integral criteria for the existence of positive solutions of first-order linear differential advanced-argument equations

Type

journal article in Web of Science

Language

en

Original Abstract

A linear differential equation with advanced-argument $y'(t)-c(t)y(t+\tau)=0$ is considered where $c\colon [t_0,\infty)\to [0,\infty)$, $t_0\in \bR$ is a bounded and locally Lipschitz continuous function and $\tau>0$. The well-known explicit integral criterion $$ \int_{t}^{t+\tau}c(s)\,\diff s\le{1}/{\e}\,,\,\,\,t\in[t_0,\infty) $$ guarantees the existence of a positive solution on $[t_0,\infty)$. The paper derives new integral criteria involving the coefficient $c$. Their independence of the previous result is discussed as well.

English abstract

A linear differential equation with advanced-argument $y'(t)-c(t)y(t+\tau)=0$ is considered where $c\colon [t_0,\infty)\to [0,\infty)$, $t_0\in \bR$ is a bounded and locally Lipschitz continuous function and $\tau>0$. The well-known explicit integral criterion $$ \int_{t}^{t+\tau}c(s)\,\diff s\le{1}/{\e}\,,\,\,\,t\in[t_0,\infty) $$ guarantees the existence of a positive solution on $[t_0,\infty)$. The paper derives new integral criteria involving the coefficient $c$. Their independence of the previous result is discussed as well.

Keywords

Positive solution, advanced-argument, integral criterion.

Released

31.01.2017

Publisher

Elsevier

ISBN

0893-9659

Periodical

APPLIED MATHEMATICS LETTERS

Year of study

72

Number

10

State

US

Pages from

40

Pages to

45

Pages count

8

URL

Documents

BibTex


@article{BUT137192,
  author="Josef {Diblík}",
  title="Integral criteria for the existence of positive solutions
of  first-order linear differential advanced-argument equations",
  annote="A linear differential equation with advanced-argument
$y'(t)-c(t)y(t+\tau)=0$
is considered
where $c\colon [t_0,\infty)\to [0,\infty)$, $t_0\in \bR$
is a bounded and locally Lipschitz continuous function and $\tau>0$.
The well-known explicit integral criterion
$$
\int_{t}^{t+\tau}c(s)\,\diff s\le{1}/{\e}\,,\,\,\,t\in[t_0,\infty)
$$
guarantees the existence of a positive solution on $[t_0,\infty)$.
The paper derives new integral criteria involving the coefficient
$c$. Their independence of the previous result is discussed as well.",
  address="Elsevier",
  chapter="137192",
  doi="10.1016/j.aml.2016.07.016",
  howpublished="print",
  institution="Elsevier",
  number="10",
  volume="72",
  year="2017",
  month="january",
  pages="40--45",
  publisher="Elsevier",
  type="journal article in Web of Science"
}