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"
}