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Statements

Subject Item
n2:RIV%2F00216305%3A26620%2F14%3APU108997%21RIV15-MSM-26620___
rdf:type
skos:Concept n17:Vysledek
rdfs:seeAlso
http://www.sciencedirect.com/science/article/pii/S0096300314005451
dcterms:description
In this paper we study the asymptotic behavior of solutions of nonlinear dynamic systems on time scales of the form $$y^\Delta(t)=f(t,y(t)),$$ where $f\colon\mathbb{T}\times\mathbb{R}^n\rightarrow\mathbb{R}^n$ and $\mathbb{T}$ is a time scale. For a given set $\Omega\subset\mathbb{T}\times\mathbb{R}^{n}$, we formulate the conditions for function $f$, which guarantee that at least one solution $y$ of the above system stays in $\Omega$. The dimension of the space of initial data generating such solutions is discussed and perturbed linear systems are considered as well. A linear system with singularity at infinity is considered as an example. In this paper we study the asymptotic behavior of solutions of nonlinear dynamic systems on time scales of the form $$y^\Delta(t)=f(t,y(t)),$$ where $f\colon\mathbb{T}\times\mathbb{R}^n\rightarrow\mathbb{R}^n$ and $\mathbb{T}$ is a time scale. For a given set $\Omega\subset\mathbb{T}\times\mathbb{R}^{n}$, we formulate the conditions for function $f$, which guarantee that at least one solution $y$ of the above system stays in $\Omega$. The dimension of the space of initial data generating such solutions is discussed and perturbed linear systems are considered as well. A linear system with singularity at infinity is considered as an example.
dcterms:title
Asymptotic behavior of solutions of systems of dynamic equations on time scales in a set whose boundary is a combination of strict egress and strict ingress points Asymptotic behavior of solutions of systems of dynamic equations on time scales in a set whose boundary is a combination of strict egress and strict ingress points
skos:prefLabel
Asymptotic behavior of solutions of systems of dynamic equations on time scales in a set whose boundary is a combination of strict egress and strict ingress points Asymptotic behavior of solutions of systems of dynamic equations on time scales in a set whose boundary is a combination of strict egress and strict ingress points
skos:notation
RIV/00216305:26620/14:PU108997!RIV15-MSM-26620___
n3:aktivita
n12:P
n3:aktivity
P(ED1.1.00/02.0068), P(EE2.3.30.0039), P(GAP201/10/1032)
n3:cisloPeriodika
6
n3:dodaniDat
n10:2015
n3:domaciTvurceVysledku
n19:6093760 n19:4066227
n3:druhVysledku
n13:J
n3:duvernostUdaju
n4:S
n3:entitaPredkladatele
n9:predkladatel
n3:idSjednocenehoVysledku
4393
n3:idVysledku
RIV/00216305:26620/14:PU108997
n3:jazykVysledku
n16:eng
n3:klicovaSlova
Time scale, Dynamic system, Asymptotic behavior of solution, Retract, Retraction, Lyapunov method
n3:klicoveSlovo
n7:Retraction n7:Lyapunov%20method n7:Asymptotic%20behavior%20of%20solution n7:Retract n7:Dynamic%20system n7:Time%20scale
n3:kodStatuVydavatele
US - Spojené státy americké
n3:kontrolniKodProRIV
[9668A14BA23F]
n3:nazevZdroje
APPLIED MATHEMATICS AND COMPUTATION
n3:obor
n20:BA
n3:pocetDomacichTvurcuVysledku
2
n3:pocetTvurcuVysledku
2
n3:projekt
n14:EE2.3.30.0039 n14:ED1.1.00%2F02.0068 n14:GAP201%2F10%2F1032
n3:rokUplatneniVysledku
n10:2014
n3:svazekPeriodika
238
n3:tvurceVysledku
Diblík, Josef Vítovec, Jiří
s:issn
0096-3003
s:numberOfPages
11
n15:doi
10.1016/j.amc.2014.04.021
n18:organizacniJednotka
26620