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

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2015

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

APPLIED MATHEMATICS AND COMPUTATION

ISSN

0096-3003

e-ISSN

1873-5649

Svazek periodika

265

Číslo periodika v rámci svazku

6

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

12

Strana od-do

358-369

Kód UT WoS článku

000358787100031

EID výsledku v databázi Scopus

2-s2.0-84930636383