Asymptotic Behaviour of a Two-Dimensional Differential System with a Finite Number of Nonconstant Delays under the Conditions of Instability
The result's identifiers
Result code in 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>
Alternative codes found
RIV/00216305:26220/12:PU98658
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Asymptotic Behaviour of a Two-Dimensional Differential System with a Finite Number of Nonconstant Delays under the Conditions of Instability
Original language description
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) >= 0 satisfying lim(t -> 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.
Czech name
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Czech description
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Classification
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
10102 - Applied mathematics
Result continuities
Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2012
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Abstract and Applied Analysis
ISSN
1085-3375
e-ISSN
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Volume of the periodical
Neuveden
Issue of the periodical within the volume
2012
Country of publishing house
US - UNITED STATES
Number of pages
20
Pages from-to
1-20
UT code for WoS article
000308166500001
EID of the result in the Scopus database
2-s2.0-84866092020