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.date.accessioned 2020-01-16T11:53:53Z dc.date.available 2020-01-16T11:53:53Z dc.date.issued 2013-11-27 cs dc.identifier.citation Boundary Value Problems. 2013, vol. 2013, issue 1, p. 1-14. en dc.identifier.issn 1687-2770 cs dc.identifier.other 103932 cs dc.identifier.uri http://hdl.handle.net/11012/184119 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.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.format text cs dc.format.extent 1-14 cs dc.format.mimetype application/pdf cs 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.uri http://creativecommons.org/licenses/by/2.0/ cs 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.subject time scale dc.subject dynamic system dc.subject delay dc.subject asymptotic behavior of solution dc.subject retract dc.subject retraction 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 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 sync.item.dbid VAV-103932 en sync.item.dbtype VAV en sync.item.insts 2020.03.31 09:58:34 en sync.item.modts 2020.03.31 07:42:38 en dc.coverage.issue 1 cs dc.coverage.volume 2013 cs dc.identifier.doi 10.1186/1687-2770-2013-260 cs dc.rights.access openAccess cs dc.rights.sherpa http://www.sherpa.ac.uk/romeo/issn/1687-2770/ cs dc.type.driver other en dc.type.status Peer-reviewed en dc.type.version publishedVersion en
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