Detail publikace

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

DIBLÍK, J. VÍTOVEC, J.

Originální název

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

Typ

článek v časopise ve Web of Science, Jimp

Jazyk

angličtina

Originální abstrakt

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.

Klíčová slova

Time scale; Dynamic system; Asymptotic behavior of solution; Retract; Retraction; Lyapunov method

Autoři

DIBLÍK, J.; VÍTOVEC, J.

Rok RIV

2014

Vydáno

4. 6. 2014

ISSN

0096-3003

Periodikum

APPLIED MATHEMATICS AND COMPUTATION

Ročník

238

Číslo

6

Stát

Spojené státy americké

Strany od

289

Strany do

299

Strany počet

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"
}