Lower and upper estimates of solutions to systems of delay dynamic equations on time scales
dc.contributor.author | Diblík, Josef | cs |
dc.contributor.author | Vítovec, Jiří | cs |
dc.coverage.issue | 1 | cs |
dc.coverage.volume | 2013 | cs |
dc.date.accessioned | 2020-08-04T11:01:51Z | |
dc.date.available | 2020-08-04T11:01:51Z | |
dc.date.issued | 2013-11-27 | cs |
dc.description.abstract | In this paper we study a system of delay dynamic equations on the time scale $\T$ of the form $$y^{\Delta}(t)=f(t,y_{\tau}(t)),$$ where $f\colon\mathbb{T}\times\mathbb{R}^n\rightarrow\mathbb{R}^n$, $y_\tau(t)=(y_1(\tau_1(t)),\ldots,y_n(\tau_n(t)))$ and $\tau_i\colon\T\rightarrow \T$, $i=1,\ldots,n$ are the delay functions. We are interested about the asymptotic behavior of solutions of mentioned system. | cs |
dc.description.abstract | In this paper we study a system of delay dynamic equations on the time scale $\T$ of the form $$y^{\Delta}(t)=f(t,y_{\tau}(t)),$$ where $f\colon\mathbb{T}\times\mathbb{R}^n\rightarrow\mathbb{R}^n$, $y_\tau(t)=(y_1(\tau_1(t)),\ldots,y_n(\tau_n(t)))$ and $\tau_i\colon\T\rightarrow \T$, $i=1,\ldots,n$ are the delay functions. We are interested about the asymptotic behavior of solutions of mentioned system. More precisely, we formulate conditions on a function $f$, which guarantee that the graph of at least one solution of above mentioned system stays in the prescribed domain. This result generalizes some previous results concerning the asymptotic behavior of solutions of non-delay systems of dynamic equations or of delay dynamic equations. A relevant example is considered. | en |
dc.format | text | cs |
dc.format.extent | 1-14 | cs |
dc.format.mimetype | application/pdf | cs |
dc.identifier.citation | Boundary Value Problems. 2013, vol. 2013, issue 1, p. 1-14. | en |
dc.identifier.doi | 10.1186/1687-2770-2013-260 | cs |
dc.identifier.issn | 1687-2770 | cs |
dc.identifier.other | 103932 | cs |
dc.identifier.uri | http://hdl.handle.net/11012/184119 | |
dc.language.iso | en | cs |
dc.publisher | Springer | cs |
dc.relation.ispartof | Boundary Value Problems | cs |
dc.relation.uri | https://link.springer.com/article/10.1186/1687-2770-2013-260 | cs |
dc.rights | Creative Commons Attribution 2.0 Generic | cs |
dc.rights.access | openAccess | cs |
dc.rights.sherpa | http://www.sherpa.ac.uk/romeo/issn/1687-2770/ | cs |
dc.rights.uri | http://creativecommons.org/licenses/by/2.0/ | cs |
dc.subject | time scale | |
dc.subject | dynamic system | |
dc.subject | delay | |
dc.subject | asymptotic behavior of solution | |
dc.subject | retract | |
dc.subject | retraction | |
dc.subject | time scale | en |
dc.subject | dynamic system | en |
dc.subject | delay | en |
dc.subject | asymptotic behavior of solution | en |
dc.subject | retract | en |
dc.subject | retraction | en |
dc.title | Lower and upper estimates of solutions to systems of delay dynamic equations on time scales | en |
dc.title.alternative | Lower and upper estimates of solutions to systems of delay dynamic equations on time scales | cs |
dc.type.driver | article | en |
dc.type.status | Peer-reviewed | en |
dc.type.version | publishedVersion | en |
sync.item.dbid | VAV-103932 | en |
sync.item.dbtype | VAV | en |
sync.item.insts | 2020.08.04 13:01:51 | en |
sync.item.modts | 2020.08.04 12:42:03 | en |
thesis.grantor | Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií. Ústav matematiky | cs |
thesis.grantor | Vysoké učení technické v Brně. Středoevropský technologický institut VUT. Kybernetika pro materiálové vědy | cs |
thesis.grantor | Vysoké učení technické v Brně. Fakulta stavební. Ústav matematiky a deskriptivní geometrie | cs |
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