Publication result 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

WoS Article

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

Key words in English

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

Authors

DIBLÍK, J.; VÍTOVEC, J.

RIV year

2014

Released

27.11.2013

Publisher

Springer

ISBN

1687-2770

Periodical

Boundary Value Problems

Volume

2013

Number

1

State

United States of America

Pages from

1

Pages to

14

Pages count

14

URL

https://link.springer.com/article/10.1186/1687-2770-2013-260

Full text in the Digital Library

http://hdl.handle.net/11012/184119

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",
  journal="Boundary Value Problems",
  year="2013",
  volume="2013",
  number="1",
  pages="1--14",
  doi="10.1186/1687-2770-2013-260",
  issn="1687-2770",
  url="https://link.springer.com/article/10.1186/1687-2770-2013-260"
}

Documents

Diblík-Vítovec2013_Article_LowerAndUpperEstimatesOfSoluti