Asymptotic behaviour of a two-dimensional differential system
with a nonconstant delay under the conditions of instability

J 2011

Asymptotic behaviour of a two-dimensional differential system with a nonconstant delay under the conditions of instability

KALAS, Josef a Josef REBENDA

Základní údaje

Originální název

Asymptotic behaviour of a two-dimensional differential system with a nonconstant delay under the conditions of instability

Autoři

KALAS, Josef a Josef REBENDA

Vydání

Mathematica Bohemica, Praha, Academy of Sciences of the Czech Rep. 2011, 0862-7959

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10101 Pure mathematics

Stát vydavatele

Česká republika

Utajení

není předmětem státního či obchodního tajemství

Odkazy

Mathematica Bohemica

Označené pro přenos do RIV

Ano

Kód RIV

RIV/00216224:14310/11:00049799

Organizační jednotka

Přírodovědecká fakulta

Klíčová slova anglicky

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

Štítky

AKR

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 6. 8. 2013 14:48, Mgr. Josef Rebenda, Ph.D.

Anotace

V originále

Several results dealing with the asymptotic behaviour of a real nonlinear two-dimensional system with a finite number of bounded nonconstant delays under the assumption of instability are presented. Conditions for the instable properties of solutions together with the conditions for the existence of bounded solutions are given. The methods are based on the transformation of the real system considered to one equation with complex-valued coefficients. Asymptotic properties are studied by means of a suitable Lyapunov-Krasovskii functional and the 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.

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 a two-dimensional differential system with a nonconstant delay under the conditions of instability. Mathematica Bohemica. Praha: Academy of Sciences of the Czech Rep., 2011, roč. 136, č. 2, s. 215-224. ISSN 0862-7959.

@article{939598,
   author = {Kalas, Josef and Rebenda, Josef},
   article_location = {Praha},
   article_number = {2},
   keywords = {delayed differential equations; asymptotic behaviour; boundedness of solutions; Lyapunov method; Wazewski topological principle},
   language = {eng},
   issn = {0862-7959},
   journal = {Mathematica Bohemica},
   title = {Asymptotic behaviour of a two-dimensional differential system with a nonconstant delay under the conditions of instability},
   url = {http://mb.math.cas.cz/},
   volume = {136},
   year = {2011}
}

TY  - JOUR
ID  - 939598
AU  - Kalas, Josef - Rebenda, Josef
PY  - 2011
TI  - Asymptotic behaviour of a two-dimensional differential system with a nonconstant delay under the conditions of instability
JF  - Mathematica Bohemica
VL  - 136
IS  - 2
SP  - 215-224
EP  - 215-224
PB  - Academy of Sciences of the Czech Rep.
SN  - 08627959
KW  - delayed differential equations
KW  - asymptotic behaviour
KW  - boundedness of solutions
KW  - Lyapunov method
KW  - Wazewski topological principle
UR  - http://mb.math.cas.cz/
N2  - Several results dealing with the asymptotic behaviour of a real nonlinear two-dimensional system with a finite number of bounded nonconstant delays under the assumption of instability are presented. Conditions for the instable properties of solutions together with the conditions for the existence of bounded solutions are given. The methods are based on the transformation of the real system considered to one equation with complex-valued coefficients. Asymptotic properties are studied by means of a suitable Lyapunov-Krasovskii functional and the 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.
ER  -

KALAS, Josef a Josef REBENDA. Asymptotic behaviour of a two-dimensional differential system with a nonconstant delay under the conditions of instability. \textit{Mathematica Bohemica}. Praha: Academy of Sciences of the Czech Rep., 2011, roč.~136, č.~2, s.~215-224. ISSN~0862-7959.

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