Lower and upper estimates of solutions to systems of delay dynamic equations on time scales

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dc.contributor.authorDiblík, Josefcs
dc.contributor.authorVítovec, Jiřícs
dc.coverage.issue1cs
dc.coverage.volume2013cs
dc.date.issued2013-11-27cs
dc.description.abstractIn 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.abstractIn 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.formattextcs
dc.format.extent1-14cs
dc.format.mimetypeapplication/pdfcs
dc.identifier.citationBoundary Value Problems. 2013, vol. 2013, issue 1, p. 1-14.en
dc.identifier.doi10.1186/1687-2770-2013-260cs
dc.identifier.issn1687-2770cs
dc.identifier.orcid0000-0001-5009-316Xcs
dc.identifier.orcid0000-0002-9510-566Xcs
dc.identifier.other103932cs
dc.identifier.researcheridD-3530-2014cs
dc.identifier.researcheridB-1353-2014cs
dc.identifier.scopus6701633618cs
dc.identifier.scopus8976321600cs
dc.identifier.urihttp://hdl.handle.net/11012/184119
dc.language.isoencs
dc.publisherSpringercs
dc.relation.ispartofBoundary Value Problemscs
dc.relation.urihttps://link.springer.com/article/10.1186/1687-2770-2013-260cs
dc.rightsCreative Commons Attribution 2.0 Genericcs
dc.rights.accessopenAccesscs
dc.rights.sherpahttp://www.sherpa.ac.uk/romeo/issn/1687-2770/cs
dc.rights.urihttp://creativecommons.org/licenses/by/2.0/cs
dc.subjecttime scaleen
dc.subjectdynamic systemen
dc.subjectdelayen
dc.subjectasymptotic behavior of solutionen
dc.subjectretracten
dc.subjectretractionen
dc.subjecttime scale
dc.subjectdynamic system
dc.subjectdelay
dc.subjectasymptotic behavior of solution
dc.subjectretract
dc.subjectretraction
dc.titleLower and upper estimates of solutions to systems of delay dynamic equations on time scalesen
dc.title.alternativeLower and upper estimates of solutions to systems of delay dynamic equations on time scalescs
dc.type.driverarticleen
dc.type.statusPeer-revieweden
dc.type.versionpublishedVersionen
sync.item.dbidVAV-103932en
sync.item.dbtypeVAVen
sync.item.insts2025.02.03 15:40:43en
sync.item.modts2025.01.17 15:13:59en
thesis.grantorVysoké učení technické v Brně. Fakulta stavební. Ústav matematiky a deskriptivní geometriecs
thesis.grantorVysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií. Ústav matematikycs
thesis.grantorVysoké učení technické v Brně. Středoevropský technologický institut VUT. Kybernetika pro materiálové vědycs
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