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

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26620%2F15%3APU114197" target="_blank" >RIV/00216305:26620/15:PU114197 - isvavai.cz</a>
Result on the web
<a href="http://www.sciencedirect.com/science/article/pii/S009630031500644X" target="_blank" >http://www.sciencedirect.com/science/article/pii/S009630031500644X</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.amc.2015.05.027" target="_blank" >10.1016/j.amc.2015.05.027</a>

Result language
angličtina
Original language name
Ważewski type theorem for non-autonomous systems of equations with a disconnected set of egress points
Original language description
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 $fcolonmathbb{T}timesmathbb{R}^nrightarrowmathbb{R}^n$, and $mathbb{T}$ is a time scale. For a given set $Omegasubsetmathbb{T}timesR^{n}$, 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 $tinmathbb{T}$) 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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>S - Specificky vyzkum na vysokych skolach

Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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