Ohraničená řešení zpožděných dynamických rovnic na časových škálách

 dc.contributor.author Diblík, Josef cs dc.contributor.author Vítovec, Jiří cs dc.date.accessioned 2019-02-13T11:57:32Z dc.date.available 2019-02-13T11:57:32Z dc.date.issued 2012-10-24 cs dc.identifier.citation Advances in Difference Equations. 2012, vol. 2012, issue 1, p. 1-9. en dc.identifier.issn 1687-1847 cs dc.identifier.other 96019 cs dc.identifier.uri http://hdl.handle.net/11012/137958 dc.description.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. en dc.description.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. cs dc.format text cs dc.format.extent 1-9 cs dc.format.mimetype application/pdf cs dc.language.iso en cs dc.publisher Springer Nature cs dc.relation.ispartof Advances in Difference Equations cs dc.relation.uri https://advancesindifferenceequations.springeropen.com/articles/10.1186/1687-1847-2012-183 cs dc.rights Creative Commons Attribution 2.0 Generic cs dc.rights.uri http://creativecommons.org/licenses/by/2.0/ cs dc.subject Asymptotic behavior en dc.subject delay dynamic equation en dc.subject time scale. en dc.subject Asymptotic behavior dc.subject delay dynamic equation dc.subject time scale. dc.title Bounded solutions of delay dynamic equations on time scales en dc.title.alternative Ohraničená řešení zpožděných dynamických rovnic na časových škálách cs thesis.grantor Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií. Ústav matematiky cs thesis.grantor Vysoké učení technické v Brně. Fakulta stavební. Ústav matematiky a deskriptivní geometrie cs sync.item.dbid VAV-96019 en sync.item.dbtype VAV en sync.item.insts 2019.06.17 10:23:32 en sync.item.modts 2019.05.18 00:33:13 en dc.coverage.issue 1 cs dc.coverage.volume 2012 cs dc.identifier.doi 10.1186/1687-1847-2012-183 cs dc.rights.access openAccess cs dc.rights.sherpa http://www.sherpa.ac.uk/romeo/issn/1687-1847/ cs dc.type.driver article en dc.type.status Peer-reviewed en dc.type.version publishedVersion en
﻿

### This item appears in the following Collection(s)

Except where otherwise noted, this item's license is described as Creative Commons Attribution 2.0 Generic