Detail publikačního výsledku

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

DIBLÍK, J.; VÍTOVEC, J.

Originální název

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

Anglický název

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

Druh

Článek WoS

Originální abstrakt

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.

Anglický abstrakt

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.

Klíčová slova

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

Klíčová slova v angličtině

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

Autoři

DIBLÍK, J.; VÍTOVEC, J.

Rok RIV

2014

Vydáno

27.11.2013

Nakladatel

Springer

ISSN

1687-2770

Periodikum

Boundary Value Problems

Svazek

2013

Číslo

1

Stát

Spojené státy americké

Strany od

1

Strany do

14

Strany počet

14

URL

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

Plný text v Digitální knihovně

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"
}

Dokumenty

Diblík-Vítovec2013_Article_LowerAndUpperEstimatesOfSoluti