Bounded solutions of delay dynamic equations on time scales

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dc.contributor.authorDiblík, Josefcs
dc.contributor.authorVítovec, Jiřícs
dc.coverage.issue1cs
dc.coverage.volume2012cs
dc.date.issued2012-10-24cs
dc.description.abstractIn 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.abstractIn 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.formattextcs
dc.format.extent1-9cs
dc.format.mimetypeapplication/pdfcs
dc.identifier.citationAdvances in Difference Equations. 2012, vol. 2012, issue 1, p. 1-9.en
dc.identifier.doi10.1186/1687-1847-2012-183cs
dc.identifier.issn1687-1847cs
dc.identifier.orcid0000-0001-5009-316Xcs
dc.identifier.orcid0000-0002-9510-566Xcs
dc.identifier.other96019cs
dc.identifier.researcheridD-3530-2014cs
dc.identifier.researcheridB-1353-2014cs
dc.identifier.scopus6701633618cs
dc.identifier.scopus8976321600cs
dc.identifier.urihttp://hdl.handle.net/11012/137958
dc.language.isoencs
dc.publisherSpringer Naturecs
dc.relation.ispartofAdvances in Difference Equationscs
dc.relation.urihttps://advancesindifferenceequations.springeropen.com/articles/10.1186/1687-1847-2012-183cs
dc.rightsCreative Commons Attribution 2.0 Genericcs
dc.rights.accessopenAccesscs
dc.rights.sherpahttp://www.sherpa.ac.uk/romeo/issn/1687-1847/cs
dc.rights.urihttp://creativecommons.org/licenses/by/2.0/cs
dc.subjectAsymptotic behavioren
dc.subjectdelay dynamic equationen
dc.subjecttime scale.en
dc.subjectAsymptotic behavior
dc.subjectdelay dynamic equation
dc.subjecttime scale.
dc.titleBounded solutions of delay dynamic equations on time scalesen
dc.title.alternativeOhraničená řešení zpožděných dynamických rovnic na časových škáláchcs
dc.type.driverarticleen
dc.type.statusPeer-revieweden
dc.type.versionpublishedVersionen
sync.item.dbidVAV-96019en
sync.item.dbtypeVAVen
sync.item.insts2025.02.03 15:40:42en
sync.item.modts2025.01.17 16:40:33en
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
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