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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" }