Detail publikačního výsledku

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

Anglický 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

Druh

Článek WoS

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.

Anglický 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

Klíčová slova v angličtině

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

Autoři

DIBLÍK, J.; VÍTOVEC, J.

Rok RIV

2015

Vydáno

04.06.2014

ISSN

0096-3003

Periodikum

APPLIED MATHEMATICS AND COMPUTATION

Svazek

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"
}