Asymptotic behaviour of solutions of real two-dimensional
differential system with nonconstant delay in an unstable case

J 2012

Asymptotic behaviour of solutions of real two-dimensional differential system with nonconstant delay in an unstable case

KALAS, Josef a Josef REBENDA

Základní údaje

Originální název

Asymptotic behaviour of solutions of real two-dimensional differential system with nonconstant delay in an unstable case

Název česky

Asymptoptické chování řešení reálného dvojrozměrného diferenciálního systému s nekonstantním zpožděním v nestabilním případě

Autoři

KALAS, Josef a Josef REBENDA

Vydání

Electronic Journal of Qualitative Theory of Differential Equations, Szeged, 2012, 1417-3875

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10101 Pure mathematics

Stát vydavatele

Maďarsko

Utajení

není předmětem státního či obchodního tajemství

Odkazy

URL

Impakt faktor

Impact factor: 0.740

Označené pro přenos do RIV

Ano

Kód RIV

RIV/00216224:14310/12:00057247

Organizační jednotka

Přírodovědecká fakulta

UT WoS

000299620000001

Klíčová slova anglicky

Delayed differential equations; asymptotic behaviour; boundedness of solutions; Lyapunov method; Wazewski topological principle

Štítky

AKR, rivok

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 9. 4. 2013 13:22, Ing. Andrea Mikešková

Anotace

V originále

The asymptotic behaviour for the solutions of a real two-dimensional system with a bounded nonconstant delay is studied under the assumption of instability. Our results improve and complement previous results by J. Kalas, where the sufficient conditions assuring the existence of bounded solutions or solutions tending to origin for t approaching infinity are given. The method of investigation is based on the transformation of the considered real system to one equation with complex-valued coefficients. Asymptotic properties of this equation are studied by means of a suitable Lyapunov-Krasovskii functional and by virtue of the Wazewski topological principle.

Návaznosti

GA201/08/0469, projekt VaV

Název: Oscilační a asymptotické vlastnosti řešení diferenciálních rovnic

Investor: Grantová agentura ČR, Oscilační a asymptotické vlastnosti řešení diferenciálních rovnic

Citovat

KALAS, Josef a Josef REBENDA. Asymptotic behaviour of solutions of real two-dimensional differential system with nonconstant delay in an unstable case. Electronic Journal of Qualitative Theory of Differential Equations. Szeged, 2012, Neuveden, č. 8, s. 1-19. ISSN 1417-3875.

@article{967835,
   author = {Kalas, Josef and Rebenda, Josef},
   article_location = {Szeged},
   article_number = {8},
   keywords = {Delayed differential equations; asymptotic behaviour; boundedness of solutions; Lyapunov method; Wazewski topological principle},
   language = {eng},
   issn = {1417-3875},
   journal = {Electronic Journal of Qualitative Theory of Differential Equations},
   title = {Asymptotic behaviour of solutions of real two-dimensional differential system with nonconstant delay in an unstable case},
   url = {http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=612},
   volume = {Neuveden},
   year = {2012}
}

TY  - JOUR
ID  - 967835
AU  - Kalas, Josef - Rebenda, Josef
PY  - 2012
TI  - Asymptotic behaviour of solutions of real two-dimensional differential system with nonconstant delay in an unstable case
JF  - Electronic Journal of Qualitative Theory of Differential Equations
VL  - Neuveden
IS  - 8
SP  - 1-19
EP  - 1-19
SN  - 14173875
KW  - Delayed differential equations
KW  - asymptotic behaviour
KW  - boundedness of solutions
KW  - Lyapunov method
KW  - Wazewski topological principle
UR  - http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=612
N2  - The asymptotic behaviour for the solutions of a real two-dimensional system with a bounded nonconstant delay is studied under the assumption of instability. Our results improve and complement previous results by J. Kalas, where the sufficient conditions assuring the existence of bounded solutions or solutions tending to origin for t approaching infinity are given. The method of investigation is based on the transformation of the considered real system to one equation with complex-valued coefficients. Asymptotic properties of this equation are studied by means of a suitable Lyapunov-Krasovskii functional and by virtue of the Wazewski topological principle.
ER  -

KALAS, Josef a Josef REBENDA. Asymptotic behaviour of solutions of real two-dimensional differential system with nonconstant delay in an unstable case. \textit{Electronic Journal of Qualitative Theory of Differential Equations}. Szeged, 2012, Neuveden, č.~8, s.~1-19. ISSN~1417-3875.

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