Detail publikace

Ważewski type theorem for non-autonomous systems of equations with a disconnected set of egress points

GABOR, G. RUSZKOWSKI, S. VÍTOVEC, J.

Originální název

Ważewski type theorem for non-autonomous systems of equations with a disconnected set of egress points

Typ

článek v časopise ve Web of Science, Jimp

Jazyk

angličtina

Originální abstrakt

In this paper we study an asymptotic behaviour 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 $\Omega\subset\mathbb{T}\times\R^{n}$, we formulate conditions for function $f$ which guarantee that at least one solution $y$ of the above system stays in $\Omega$. Unlike previous papers the set $\Omega$ is considered in more general form, i.e., the time section $\Omega_t$ is an arbitrary closed bounded set homeomorphic to the disk (for every $t\in\mathbb{T}$) and the boundary $\partial_\mathbb{T}\Omega$ does not contain only egress points. Thanks to this, we can investigate a substantially wider range of equations with various types of bounded solutions. A relevant example is considered. The results are new also for non-autonomous systems of difference equations and the systems of impulsive differential equations.

Klíčová slova

Time scale; Dynamic system; Non-autonomous system; Difference equation; Asymptotic behavior of solution; Retract method

Autoři

GABOR, G.; RUSZKOWSKI, S.; VÍTOVEC, J.

Rok RIV

2015

Vydáno

2. 6. 2015

ISSN

0096-3003

Periodikum

APPLIED MATHEMATICS AND COMPUTATION

Ročník

265

Číslo

6

Stát

Spojené státy americké

Strany od

358

Strany do

369

Strany počet

12

URL

http://www.sciencedirect.com/science/article/pii/S009630031500644X

BibTex

@article{BUT114696,
  author="Jiří {Vítovec} and Grzegorz {Gabor} and Sebastian {Ruszkowski}",
  title="Ważewski type theorem for non-autonomous systems of equations with a disconnected set of egress points",
  journal="APPLIED MATHEMATICS AND COMPUTATION",
  year="2015",
  volume="265",
  number="6",
  pages="358--369",
  doi="10.1016/j.amc.2015.05.027",
  issn="0096-3003",
  url="http://www.sciencedirect.com/science/article/pii/S009630031500644X"
}