Detail publikačního výsledku

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

DIBLÍK, J.

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 $\dot x(t) =-c(t)x(t-\tau(t))$

Druh

Článek WoS

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.

Klíčová slova

time delay, linear differential equation, positive solution, integral criterion

Klíčová slova v angličtině

time delay, linear differential equation, positive solution, integral criterion

Autoři

DIBLÍK, J.

Rok RIV

2016

Vydáno

06.06.2015

Nakladatel

Elsevier

ISSN

0001-8708

Periodikum

ADVANCES IN MATHEMATICS

Svazek

280

Číslo

1

Stát

Spojené státy americké

Strany od

1

Strany do

20

Strany počet

20

URL

https://www.sciencedirect.com/science/article/pii/S000187081500136X

BibTex

@article{BUT115049,
  author="Josef {Diblík}",
  title="Explicit integral criteria for the existence of positive solutions of the linear delayed equation $\dot x(t) =-c(t)x(t-\tau(t))$",
  journal="ADVANCES IN MATHEMATICS",
  year="2015",
  volume="280",
  number="1",
  pages="1--20",
  doi="10.1016/j.aim.2015.04.013",
  issn="0001-8708",
  url="https://www.sciencedirect.com/science/article/pii/S000187081500136X"
}