Detail publikačního výsledku

Bounded solutions of delay dynamic equations on time scales

DIBLÍK, J.; VÍTOVEC, J.

Originální název

Bounded solutions of delay dynamic equations on time scales

Anglický název

Bounded solutions of delay dynamic equations on time scales

Druh

Článek recenzovaný mimo WoS a Scopus

Originální abstrakt

In this paper we discuss the asymptotic behavior of solutions of a delay dynamic equation $$y^{\Delta}(t)=f(t,y(\tau(t)))$$ where $f\colon\mathbb{T}\times\mathbb{R}\rightarrow\mathbb{R}$, \tau\colon\T\rightarrow \T$ is a delay function and $\mathbb{T}$ is a time scale. We formulate a principle which gives the guarantee that the graph of at least one solution of above mentioned equation stays in the prescribed domain. This principle uses the idea of the retraction method and is a suitable tool for investigating the asymptotic behavior of solutions of dynamic equations. This is illustrated by an example.

Anglický abstrakt

In this paper we discuss the asymptotic behavior of solutions of a delay dynamic equation $$y^{\Delta}(t)=f(t,y(\tau(t)))$$ where $f\colon\mathbb{T}\times\mathbb{R}\rightarrow\mathbb{R}$, \tau\colon\T\rightarrow \T$ is a delay function and $\mathbb{T}$ is a time scale. We formulate a principle which gives the guarantee that the graph of at least one solution of above mentioned equation stays in the prescribed domain. This principle uses the idea of the retraction method and is a suitable tool for investigating the asymptotic behavior of solutions of dynamic equations. This is illustrated by an example.

Klíčová slova

Asymptotic behavior, delay dynamic equation, time scale.

Klíčová slova v angličtině

Asymptotic behavior, delay dynamic equation, time scale.

Autoři

DIBLÍK, J.; VÍTOVEC, J.

Rok RIV

2013

Vydáno

24.10.2012

Nakladatel

Springer Nature

ISSN

1687-1847

Periodikum

Advances in Difference Equations

Svazek

2012

Číslo

1

Stát

Spojené státy americké

Strany od

1

Strany do

9

Strany počet

9

URL

https://advancesindifferenceequations.springeropen.com/articles/10.1186/1687-1847-2012-183

Plný text v Digitální knihovně

http://hdl.handle.net/11012/137958

BibTex

@article{BUT96019,
  author="Josef {Diblík} and Jiří {Vítovec}",
  title="Bounded solutions of delay dynamic equations on time scales",
  journal="Advances in Difference Equations",
  year="2012",
  volume="2012",
  number="1",
  pages="1--9",
  doi="10.1186/1687-1847-2012-183",
  issn="1687-1847",
  url="https://advancesindifferenceequations.springeropen.com/articles/10.1186/1687-1847-2012-183"
}

Dokumenty

1687-1847-2012-183