Přístupnostní navigace
E-application
Search Search Close
Publication detail
GABOR, G. RUSZKOWSKI, S. VÍTOVEC, J.
Original Title
Ważewski type theorem for non-autonomous systems of equations with a disconnected set of egress points
Type
journal article in Web of Science
Language
English
Original Abstract
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.
Keywords
Time scale; Dynamic system; Non-autonomous system; Difference equation; Asymptotic behavior of solution; Retract method
Authors
GABOR, G.; RUSZKOWSKI, S.; VÍTOVEC, J.
RIV year
2015
Released
2. 6. 2015
ISBN
0096-3003
Periodical
APPLIED MATHEMATICS AND COMPUTATION
Year of study
265
Number
6
State
United States of America
Pages from
358
Pages to
369
Pages count
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" }