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  • 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.
  • 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. (en)
Title
  • Asymptotic behaviour of solutions of real two-dimensional differential system with nonconstant delay in an unstable case
  • Asymptotic behaviour of solutions of real two-dimensional differential system with nonconstant delay in an unstable case (en)
skos:prefLabel
  • Asymptotic behaviour of solutions of real two-dimensional differential system with nonconstant delay in an unstable case
  • Asymptotic behaviour of solutions of real two-dimensional differential system with nonconstant delay in an unstable case (en)
skos:notation
  • RIV/00216224:14310/12:00057247!RIV13-GA0-14310___
http://linked.open...avai/riv/aktivita
http://linked.open...avai/riv/aktivity
  • P(GA201/08/0469)
http://linked.open...iv/cisloPeriodika
  • 8
http://linked.open...vai/riv/dodaniDat
http://linked.open...aciTvurceVysledku
http://linked.open.../riv/druhVysledku
http://linked.open...iv/duvernostUdaju
http://linked.open...titaPredkladatele
http://linked.open...dnocenehoVysledku
  • 123966
http://linked.open...ai/riv/idVysledku
  • RIV/00216224:14310/12:00057247
http://linked.open...riv/jazykVysledku
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  • Delayed differential equations; asymptotic behaviour; boundedness of solutions; Lyapunov method; Wazewski topological principle (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...odStatuVydavatele
  • HU - Maďarsko
http://linked.open...ontrolniKodProRIV
  • [B70E58626F24]
http://linked.open...i/riv/nazevZdroje
  • Electronic Journal of Qualitative Theory of Differential Equations
http://linked.open...in/vavai/riv/obor
http://linked.open...ichTvurcuVysledku
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http://linked.open...vavai/riv/projekt
http://linked.open...UplatneniVysledku
http://linked.open...v/svazekPeriodika
  • Neuveden
http://linked.open...iv/tvurceVysledku
  • Kalas, Josef
  • Rebenda, Josef
http://linked.open...ain/vavai/riv/wos
  • 000299620000001
issn
  • 1417-3875
number of pages
http://localhost/t...ganizacniJednotka
  • 14310
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