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

Diblík, Josef; Růžičková, Miroslava; Šmarda, Zdeněk; Šutá, Zuzana

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

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580750.pdf(1.89 MB)

Date

2012-01-03

Authors

Publisher

Hindawi

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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.
Je dokázáno, že pro asymptotickou konvergenci všech řešení je postačující existence rostoucího asymptoticky konvergentního řešení. Hlavní pozornost je tedy věnována kritériím existence rostoucího asymptoticky konvergentního řešení.

Keywords

difference equation, asymptotically convergent solution, auxiliary inequality, diferenční rovnice, asymptoticky konvergentní řešení, pomocná nerovnost

Citation

Abstract and Applied Analysis. 2012, vol. 2012, issue ID 580750, p. 1-20.
https://www.hindawi.com/journals/aaa/2012/580750/

Document type

Peer-reviewed

Document version

Published version

Language of document

en