Publication detail

# Unbounded solutions of the equation $\dot y(t)=\sum_{i=1}^{n}\beta_{i}$ (t)\left[y(t-\delta_{i})-y(t-\tau_{i})\right]$

DIBLÍK, J. RŮŽIČKOVÁ, M. CHUPÁČ, R.

Original Title

Unbounded solutions of the equation $\dot y(t)=\sum_{i=1}^{n}\beta_{i}$ (t)\left[y(t-\delta_{i})-y(t-\tau_{i})\right]$

English Title

Unbounded solutions of the equation $\dot y(t)=\sum_{i=1}^{n}\beta_{i}$ (t)\left[y(t-\delta_{i})-y(t-\tau_{i})\right]$

Type

journal article - other

Language

en

Original Abstract

Asymptotic behavior of solutions of first-order differential equation with deviating arguments in the form $\dot y(t)=\sum_{i=1}^{n}\beta_{i}(t)\left[y(t-\delta_{i})-y(t-\tau_{i})\right]$ is discussed for $t\to\infty$. A criterion for representing solutions in exponential form is proved. Inequalities for solution estimation are given. Sufficient conditions for the existence of unbounded solutions are derived. A relevant illustrative example is given as well. Known results are discussed and compared.

English abstract

Asymptotic behavior of solutions of first-order differential equation with deviating arguments in the form $\dot y(t)=\sum_{i=1}^{n}\beta_{i}(t)\left[y(t-\delta_{i})-y(t-\tau_{i})\right]$ is discussed for $t\to\infty$. A criterion for representing solutions in exponential form is proved. Inequalities for solution estimation are given. Sufficient conditions for the existence of unbounded solutions are derived. A relevant illustrative example is given as well. Known results are discussed and compared.

Keywords

Unbounded solution; exponential solution; discrete delays

RIV year

2013

Released

03.12.2013

Publisher

Elsevier Science Publishing Co

Location

USA

ISBN

0096-3003

Periodical

APPLIED MATHEMATICS AND COMPUTATION

Year of study

2013

Number

221

State

US

Pages from

610

Pages to

619

Pages count

10

Documents

BibTex

```
@article{BUT103938,
author="Josef {Diblík} and Miroslava {Růžičková} and Radoslav {Chupáč}",
title="Unbounded solutions of the equation $\dot y(t)=\sum_{i=1}^{n}\beta_{i}$ (t)\left[y(t-\delta_{i})-y(t-\tau_{i})\right]$",
annote="Asymptotic behavior of solutions of first-order differential equation with deviating arguments in the form $\dot y(t)=\sum_{i=1}^{n}\beta_{i}(t)\left[y(t-\delta_{i})-y(t-\tau_{i})\right]$ is discussed for $t\to\infty$. A criterion for representing solutions in exponential form is proved. Inequalities for solution estimation are given. Sufficient conditions for the existence of unbounded solutions are derived. A relevant illustrative example is given as well. Known results are discussed and compared.",
address="Elsevier Science Publishing Co",
chapter="103938",
institution="Elsevier Science Publishing Co",
number="221",
volume="2013",
year="2013",
month="december",
pages="610--619",
publisher="Elsevier Science Publishing Co",
type="journal article - other"
}
```