Publication detail

# Lower and upper estimates of solutions to systems of delay dynamic equations on time scales

DIBLÍK, J. VÍTOVEC, J.

Original Title

Lower and upper estimates of solutions to systems of delay dynamic equations on time scales

English Title

Lower and upper estimates of solutions to systems of delay dynamic equations on time scales

Type

journal article in Web of Science

Language

en

Original Abstract

In this paper we study a system of delay dynamic equations on the time scale $\T$ of the form $$y^{\Delta}(t)=f(t,y_{\tau}(t)),$$ where $f\colon\mathbb{T}\times\mathbb{R}^n\rightarrow\mathbb{R}^n$, $y_\tau(t)=(y_1(\tau_1(t)),\ldots,y_n(\tau_n(t)))$ and $\tau_i\colon\T\rightarrow \T$, $i=1,\ldots,n$ are the delay functions. We are interested about the asymptotic behavior of solutions of mentioned system. More precisely, we formulate conditions on a function $f$, which guarantee that the graph of at least one solution of above mentioned system stays in the prescribed domain. This result generalizes some previous results concerning the asymptotic behavior of solutions of non-delay systems of dynamic equations or of delay dynamic equations. A relevant example is considered.

English abstract

In this paper we study a system of delay dynamic equations on the time scale $\T$ of the form $$y^{\Delta}(t)=f(t,y_{\tau}(t)),$$ where $f\colon\mathbb{T}\times\mathbb{R}^n\rightarrow\mathbb{R}^n$, $y_\tau(t)=(y_1(\tau_1(t)),\ldots,y_n(\tau_n(t)))$ and $\tau_i\colon\T\rightarrow \T$, $i=1,\ldots,n$ are the delay functions. We are interested about the asymptotic behavior of solutions of mentioned system. More precisely, we formulate conditions on a function $f$, which guarantee that the graph of at least one solution of above mentioned system stays in the prescribed domain. This result generalizes some previous results concerning the asymptotic behavior of solutions of non-delay systems of dynamic equations or of delay dynamic equations. A relevant example is considered.

Keywords

time scale; dynamic system; delay; asymptotic behavior of solution; retract; retraction

RIV year

2013

Released

27.11.2013

Publisher

Springer

ISBN

1687-2770

Periodical

Boundary Value Problems

Year of study

2013

Number

1

State

US

Pages from

1

Pages to

14

Pages count

14

URL

Full text in the Digital Library

Documents

BibTex

```
@article{BUT103932,
author="Josef {Diblík} and Jiří {Vítovec}",
title="Lower and upper estimates of solutions to systems of delay dynamic equations on time scales",
annote="In this paper we study a system of delay dynamic equations on the time scale $\T$ of the form $$y^{\Delta}(t)=f(t,y_{\tau}(t)),$$ where $f\colon\mathbb{T}\times\mathbb{R}^n\rightarrow\mathbb{R}^n$, $y_\tau(t)=(y_1(\tau_1(t)),\ldots,y_n(\tau_n(t)))$ and $\tau_i\colon\T\rightarrow \T$, $i=1,\ldots,n$ are the delay functions. We are interested about the asymptotic behavior of solutions of mentioned system. More precisely, we formulate conditions on a function $f$, which
guarantee that the graph of at least one solution of above mentioned system stays in the prescribed domain. This result generalizes some previous results concerning the asymptotic behavior of solutions of non-delay systems of dynamic equations or of delay dynamic equations. A relevant example is considered.",
address="Springer",
chapter="103932",
doi="10.1186/1687-2770-2013-260",
institution="Springer",
number="1",
volume="2013",
year="2013",
month="november",
pages="1--14",
publisher="Springer",
type="journal article in Web of Science"
}
```