Detail publikace

# Explicit integral criteria for the existence of positive solutions of the linear delayed equation $\dot x(t) =-c(t)x(t-\tau(t))$

Originální název

Explicit integral criteria for the existence of positive solutions of the linear delayed equation $\dot x(t) =-c(t)x(t-\tau(t))$

Anglický název

Explicit integral criteria for the existence of positive solutions of the linear delayed equation $\dot x(t) =-c(t)x(t-\tau(t))$

Jazyk

en

Originální abstrakt

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.

Anglický abstrakt

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.

Dokumenty

BibTex


@article{BUT115049,
author="Josef {Diblík}",
title="Explicit integral criteria for the existence of positive solutions of the linear delayed equation $\dot x(t) =-c(t)x(t-\tau(t))$",
annote="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.",
}