Detail publikačního výsledku

Long-Time Behavior of Positive Solutions of a Differential Equation with State-Dependent Delay

DIBLÍK, J.

Originální název

Long-Time Behavior of Positive Solutions of a Differential Equation with State-Dependent Delay

Anglický název

Long-Time Behavior of Positive Solutions of a Differential Equation with State-Dependent Delay

Druh

Článek WoS

Originální abstrakt

Abstract. The long-time behavior of positive solutions of a differential equation with state-dependent delay y'(t) = −c(t)y(t − τ(t, y(t))), where c is a positive coefficient, is considered. Sufficient conditions are given for the existence of positive solutions bounded from below and from above by functions of exponential type. As a consequence, criteria for the existence of positive solutions are derived and their lower bounds are given. Relationships are discussed with the existing results on the existence of positive solutions for delayed differential equations.

Anglický abstrakt

Abstract. The long-time behavior of positive solutions of a differential equation with state-dependent delay y'(t) = −c(t)y(t − τ(t, y(t))), where c is a positive coefficient, is considered. Sufficient conditions are given for the existence of positive solutions bounded from below and from above by functions of exponential type. As a consequence, criteria for the existence of positive solutions are derived and their lower bounds are given. Relationships are discussed with the existing results on the existence of positive solutions for delayed differential equations.

Klíčová slova

Long-time behavior; time-dependent delay; exponential estimation of solutions; positive solution; monotone iterative method.

Klíčová slova v angličtině

Long-time behavior; time-dependent delay; exponential estimation of solutions; positive solution; monotone iterative method.

Autoři

DIBLÍK, J.

Rok RIV

2021

Vydáno

01.01.2020

Nakladatel

AMER INST MATHEMATICAL SCIENCES-AIMS, PO BOX 2604, SPRINGFIELD, MO 65801-2604 USA

Místo

USA

ISSN

1937-1632

Periodikum

Discrete and Continuous Dynamical Systems-Series S

Svazek

13

Číslo

1

Stát

Spojené státy americké

Strany od

31

Strany do

46

Strany počet

16

URL

http://www.aimsciences.org/article/doi/10.3934/dcdss.2020002

BibTex

@article{BUT165826,
  author="Josef {Diblík}",
  title="Long-Time Behavior of Positive Solutions of a Differential Equation with State-Dependent Delay",
  journal="Discrete and Continuous Dynamical Systems-Series S",
  year="2020",
  volume="13",
  number="1",
  pages="31--46",
  doi="10.3934/dcdss.2020002",
  issn="1937-1632",
  url="http://www.aimsciences.org/article/doi/10.3934/dcdss.2020002"
}