Publication detail

Solutions of an advance-delay differential equation and their asymptotic behaviour

VÁŽANOVÁ, G.

Original Title

Solutions of an advance-delay differential equation and their asymptotic behaviour

Type

journal article in Web of Science

Language

English

Original Abstract

The paper considers a scalar differential equation of an advance-delay type \begin{equation*} \dot{y}(t)= -\left(a_0+\frac{a_1}{t}\right)y(t-\tau )+\left(b_0+\frac{b_1}{t}\right)y(t+\sigma )\,, \end{equation*} where constants $a_0$, $b_0$, $\tau $ and $\sigma $ are positive, and $a_1$ and $b_1$ are arbitrary. The behavior of its solutions for $t\rightarrow \infty $ is analyzed provided that the transcendental equation \begin{equation*} \lambda = -a_0\mathrm{e}^{-\lambda \tau }+b_0\mathrm{e}^{\lambda \sigma } \end{equation*} has a positive real root. An exponential-type function approximating the solution is searched for to be used in proving the existence of a semi-global solution. Moreover, the lower and upper estimates are given for such a solution.

Keywords

advance-delay differential equation; mixed-type differential equation; asymptotic behaviour; existence of solutions

Authors

VÁŽANOVÁ, G.

Released

28. 2. 2023

Location

Brno

ISBN

1212-5059

Periodical

Archivum Mathematicum

Year of study

59

Number

1

State

Czech Republic

Pages from

141

Pages to

149

Pages count

9

URL

https://dml.cz/handle/10338.dmlcz/151559

BibTex

@article{BUT185052,
  author="Gabriela {Vážanová}",
  title="Solutions of an advance-delay differential equation and their asymptotic behaviour",
  journal="Archivum Mathematicum",
  year="2023",
  volume="59",
  number="1",
  pages="141--149",
  doi="10.5817/AM2023-1-141",
  issn="1212-5059",
  url="https://dml.cz/handle/10338.dmlcz/151559"
}