Publication detail

Bounded solutions of delay dynamic equations on time scales

DIBLÍK, J. VÍTOVEC, J.

Original Title

Bounded solutions of delay dynamic equations on time scales

English Title

Bounded solutions of delay dynamic equations on time scales

Type

journal article - other

Language

en

Original Abstract

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.

English abstract

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.

Keywords

Asymptotic behavior, delay dynamic equation, time scale.

RIV year

2012

Released

24.10.2012

Publisher

Springer Nature

ISBN

1687-1847

Periodical

Advances in Difference Equations

Year of study

2012

Number

1

State

US

Pages from

1

Pages to

9

Pages count

9

URL

Full text in the Digital Library

Documents

BibTex


@article{BUT96019,
  author="Josef {Diblík} and Jiří {Vítovec}",
  title="Bounded solutions of delay dynamic equations on time scales",
  annote="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.",
  address="Springer Nature",
  chapter="96019",
  doi="10.1186/1687-1847-2012-183",
  institution="Springer Nature",
  number="1",
  volume="2012",
  year="2012",
  month="october",
  pages="1--9",
  publisher="Springer Nature",
  type="journal article - other"
}