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On the asymptotics of the difference equation with a proportional delay

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Języki publikacji
EN
Abstrakty
EN
This paper deals with asymptotic properties of a vector difference equation with delayed argument Δxk = Axk +Bx(λk], 0 < λ < 1, k = 0,1,2,..., where A, B are constant matrices and the term [λk] is the integer part of λk. Our aim is to emphasize some resemblances between the asymptotic behaviour of this delay difference equation and its continuous counterpart.
Rocznik
Strony
499--506
Opis fizyczny
Bibliogr. 13 poz., rys., wykr.
Twórcy
autor
  • Brno Univeristy of Technology, Institute of Mathematics, Technická 2, 61669 Brno, Czech Republik, kundrat@fme.vutbr.cz
Bibliografia
  • [1] A. Bellen, M. Zennaro, Numerical Methods for Delay Differential Equations, Clarendon Press, Oxford, 2003.
  • [2] J. Cermak, The Asymptotics of Solutions for a Class of Delay Differential Equations, Rocky Mountain J. Mathematics 33 (2003), 775-786.
  • [3] I. Gyori, M. Pituk, Comparison Theorems and Asymptotic Equilibrium for Delay Differential and Difference Equations, Dynam. Systems Appl. 5 (1996), 277-302.
  • [4] A. Iserles, On the Generalized Pantograph Functional-Differential Equation, European J. Appl. Math. 4 (1993), 1-38.
  • [5] A. Iserles, Exact and Discretized Stability of the Pantograph Equation, Appl. Numer. Math. 24 (1997), 295-308.
  • [6] T. Kato, J. B. McLeod, The Functional Differential Equation y'(x) = ay(lambdax) + by(x), Bull. Amer. Math. Soc. 77 (1971), 891-937.
  • [7] P. Kundrat, The Asymptotic Properties of Solutions of Linear Delay Differential Equations, Math. Slovaca 56 No. 3 (2006), 349-360.
  • [8] H. Lehninger, Y. Liu, The Functional-Differential Equation y'(t) = Ay(t) + By(qt) + Cy'(qt) + f(t), European J. Appl. Math. 9 (1998), 81-91.
  • [9] E. B. Lim, Asymptotic Behavior of Solutions of the Functional Differential Equation x'(t) = Ax(lambdat) + Bx(t), lambda > 0, J. Math. Anal. Appl. 55 (1976), 794-808.
  • [10] Y. Liu, Numerical Investigation of the Pantograph Equation, Appl. Numer. Math. 24 (1997), 309-317.
  • [11] G. Makay, J. Terjeki, On the Asymptotic Behavior of the Pantograph Equations, Electron J. Qual. Theory Differ. Equ. 2 (1998), 1-12 [electronic].
  • [12] J. R. Ockendon, A. B. Tayler, The Dynamics of a Current Collection System for an Electric Locomotive, In: Proc. Roy. Soc. Lond. A. 322 (1971), 447-468.
  • [13] H. Peics, On the Asymptotic Behaviour of Difference Equations with Continuous Arguments, Ser A. Math. Anal. 9 No. 2 (2002), 257-273.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-AGH4-0007-0100
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