Publication detail

Asymptotic convergence of the solutions of a dynamic equation on discrete time scales

DIBLÍK, J. RŮŽIČKOVÁ, M. ŠMARDA, Z. ŠUTÁ, Z.

Original Title

Asymptotic convergence of the solutions of a dynamic equation on discrete time scales

English Title

Asymptotic convergence of the solutions of a dynamic equation on discrete time scales

Type

journal article

Language

en

Original Abstract

It is proved that, for the asymptotic convergence of all solutions, the existence of an increasing and asymptotically convergent solution is sufficient. Therefore, the main attention is paid to the criteria for the existence of an increasing solution asymptotically convergent for n goes to infinity. The results are presented as inequalities for the function beta. Examples demonstrate that the criteria obtained are sharp in a sense.

English abstract

It is proved that, for the asymptotic convergence of all solutions, the existence of an increasing and asymptotically convergent solution is sufficient. Therefore, the main attention is paid to the criteria for the existence of an increasing solution asymptotically convergent for n goes to infinity. The results are presented as inequalities for the function beta. Examples demonstrate that the criteria obtained are sharp in a sense.

Keywords

difference equation, asymptotically convergent solution, auxiliary inequality

RIV year

2012

Released

03.01.2012

Publisher

Hindawi

Location

USA

Pages from

1

Pages to

20

Pages count

20

URL

Full text in the Digital Library

BibTex


@article{BUT74921,
  author="Josef {Diblík} and Miroslava {Růžičková} and Zdeněk {Šmarda} and Zuzana {Šutá}",
  title="Asymptotic convergence of the solutions of a dynamic equation on discrete time scales",
  annote="It is proved that, for the asymptotic convergence of all solutions, the existence of
an increasing and asymptotically convergent solution is sufficient. Therefore, the main
attention is paid to the criteria for the existence of an increasing solution asymptotically
convergent for n goes to infinity. The results are presented as inequalities for the function
beta. Examples demonstrate that the criteria obtained are sharp in a sense.",
  address="Hindawi",
  chapter="74921",
  doi="10.1155/2012/580750",
  institution="Hindawi",
  number="ID 580750",
  volume="2012",
  year="2012",
  month="january",
  pages="1--20",
  publisher="Hindawi",
  type="journal article"
}