Detail publikace

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

Originální název

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

Anglický název

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

Jazyk

en

Originální abstrakt

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.

Anglický abstrakt

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.

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.",
}