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DIBLÍK, J. VÍTOVEC, J.
Original 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
Type
journal article in Web of Science
Language
English
Original Abstract
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.
Keywords
Time scale; Dynamic system; Asymptotic behavior of solution; Retract; Retraction; Lyapunov method
Authors
DIBLÍK, J.; VÍTOVEC, J.
RIV year
2014
Released
4. 6. 2014
ISBN
0096-3003
Periodical
APPLIED MATHEMATICS AND COMPUTATION
Year of study
238
Number
6
State
United States of America
Pages from
289
Pages to
299
Pages count
11
URL
http://www.sciencedirect.com/science/article/pii/S0096300314005451
BibTex
@article{BUT107428, author="Josef {Diblík} and Jiří {Vítovec}", 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", journal="APPLIED MATHEMATICS AND COMPUTATION", year="2014", volume="238", number="6", pages="289--299", doi="10.1016/j.amc.2014.04.021", issn="0096-3003", url="http://www.sciencedirect.com/science/article/pii/S0096300314005451" }