Publication detail

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

DIBLÍK, J.

Original Title

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

English Title

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

Type

journal article in Web of Science

Language

en

Original Abstract

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.

English abstract

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.

Keywords

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

Released

01.01.2020

Publisher

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

Location

USA

ISBN

1937-1632

Periodical

Discrete and Continuous Dynamical Systems - Series S

Year of study

13

Number

1

State

US

Pages from

31

Pages to

46

Pages count

16

URL

Documents

BibTex


@article{BUT165826,
  author="Josef {Diblík}",
  title="Long-Time Behavior of Positive Solutions of a Differential Equation with State-Dependent Delay",
  annote="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.",
  address="AMER INST MATHEMATICAL SCIENCES-AIMS, PO BOX 2604, SPRINGFIELD, MO 65801-2604 USA",
  chapter="165826",
  doi="10.3934/dcdss.2020002",
  howpublished="print",
  institution="AMER INST MATHEMATICAL SCIENCES-AIMS, PO BOX 2604, SPRINGFIELD, MO 65801-2604 USA",
  number="1",
  volume="13",
  year="2020",
  month="january",
  pages="31--46",
  publisher="AMER INST MATHEMATICAL SCIENCES-AIMS, PO BOX 2604, SPRINGFIELD, MO 65801-2604 USA",
  type="journal article in Web of Science"
}