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
Type
journal article in Web of Science
Language
English
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.
Keywords
Positive solution, advanced-argument, integral criterion.
Authors
DIBLÍK, J.
Released
31. 1. 2017
Publisher
Elsevier
ISBN
0893-9659
Periodical
APPLIED MATHEMATICS LETTERS
Year of study
72
Number
10
State
United States of America
Pages from
40
Pages to
45
Pages count
8
URL
BibTex
@article{BUT137192,
author="Josef {Diblík}",
title="Integral criteria for the existence of positive solutions
of first-order linear differential advanced-argument equations",
journal="APPLIED MATHEMATICS LETTERS",
year="2017",
volume="72",
number="10",
pages="40--45",
doi="10.1016/j.aml.2016.07.016",
issn="0893-9659",
url="https://doi.org/10.1016/j.aml.2016.07.016"
}