Asymptotic Behaviour of a Two-Dimensional Differential System with a Finite Number of Nonconstant Delays under the Conditions of Instability

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F12%3A00113901" target="_blank" >RIV/00216224:14310/12:00113901 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/00216305:26220/12:PU98658

Výsledek na webu

<a href="https://www.hindawi.com/journals/aaa/2012/952601/" target="_blank" >https://www.hindawi.com/journals/aaa/2012/952601/</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1155/2012/952601" target="_blank" >10.1155/2012/952601</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Asymptotic Behaviour of a Two-Dimensional Differential System with a Finite Number of Nonconstant Delays under the Conditions of Instability

Popis výsledku v původním jazyce

The asymptotic behaviour of a real two- dimensional differential system x,(t) = A(t)x(t) + Sigma(m)(k=1) B-k(t)x(theta(k)(t)) + h(t, x (t), x(theta(1)(t)),..., x(theta(m)(t))) with unbounded nonconstant delays t-theta(k)(t) &gt;= 0 satisfying lim(t -&gt; infinity)theta(k)(t) = infinity is studied under the assumption of instability. Here, A, B-k, and h are supposed to be matrix functions and a vector function. The conditions for the instable properties of solutions and the conditions for the existence of bounded solutions are given. The methods are based on the transformation of the considered real system to one equation with complex-valued coefficients. Asymptotic properties are studied by means of a Lyapunov-Krasovskii functional and the suitable Wazewski topological principle. The results generalize some previous ones, where the asymptotic properties for two- dimensional systems with one constant or nonconstant delay were studied.

Název v anglickém jazyce

Asymptotic Behaviour of a Two-Dimensional Differential System with a Finite Number of Nonconstant Delays under the Conditions of Instability

Popis výsledku anglicky

The asymptotic behaviour of a real two- dimensional differential system x,(t) = A(t)x(t) + Sigma(m)(k=1) B-k(t)x(theta(k)(t)) + h(t, x (t), x(theta(1)(t)),..., x(theta(m)(t))) with unbounded nonconstant delays t-theta(k)(t) &gt;= 0 satisfying lim(t -&gt; infinity)theta(k)(t) = infinity is studied under the assumption of instability. Here, A, B-k, and h are supposed to be matrix functions and a vector function. The conditions for the instable properties of solutions and the conditions for the existence of bounded solutions are given. The methods are based on the transformation of the considered real system to one equation with complex-valued coefficients. Asymptotic properties are studied by means of a Lyapunov-Krasovskii functional and the suitable Wazewski topological principle. The results generalize some previous ones, where the asymptotic properties for two- dimensional systems with one constant or nonconstant delay were studied.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2012

Kód důvěrnosti údajů

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

Název periodika

Abstract and Applied Analysis

ISSN

1085-3375

e-ISSN

—

Svazek periodika

Neuveden

Číslo periodika v rámci svazku

2012

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

20

Strana od-do

1-20

Kód UT WoS článku

000308166500001

EID výsledku v databázi Scopus

2-s2.0-84866092020