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The asymptotic properties of the dynamic equation with a delayed argument

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EN
Abstrakty
EN
In this paper, we present some asymptotic results related to the scalar dynamic equation with a delayed argument. Using the time scale calculus we generalize some results known in the differential and difference case to the more general dynamie case.
Słowa kluczowe
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Strony
421--429
Opis fizyczny
Bibliogr. 18 poz.
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autor
autor
  • Brno University of Technology, Faculty of Mechanical Engineering, Department of Mathematics, Technická 2, 616 69 Brno, Czech Republic, cermak.j@fme.vutbr.cz
Bibliografia
  • [1] O. Arino, M. Pituk: More on linear differential systems with small delays, J. Differential Equations 170 (2001), 381-407.
  • [2] F.V. Atkinson, J.R. Haddock: Criteria for asymptotic constancy of solutions of functional differential equations, J. Math. Anal. Appl. 91 (1983), 410-423.
  • [3] M. Bohner: Some oscillation criteria for first order delay dynamic equations, Far East J. Appl. Math. 18(3) (2005), 289-304.
  • [4] M. Bohner, A. Peterson: Dynamic Equations on Time Scales - An Introduction With Applications. Birkhauser, Boston, 2001.
  • [5] M. Bohner, A. Peterson: Advances in Dynamic Equations on Time Scales. Birkhauser, Boston, 2003.
  • [6] J. Cermak: The asymptotic of solutions for a class of delay differential equations, Rocky Mountain J. Math. 33 (2003), 775-786.
  • [7] N.G. De Bruijn: The asymptotically periodic behavior of the solutions of some linear functional equations, Amer. J. Math., 71 (1949), 313-330.
  • [8] J. Diblik: Asymptotic representation of solutions of equation y(t) = B(t)[y(t) - y(t -r(t))], J. Math. Anal. Appl. 217 (1998), 200-215.
  • [9] I. Gyori, M. Pituk: Comparison theorems and asymptotic equilibrium for delay differential and difference equations, Dynam. Systems Appl. 5 (1996), 277-302.
  • [10] A. Iserles: On generalized pantograph functional-differential equation, European J. Appl. Math. 4 (1993), 1-38.
  • [11] M.L. Heard: A change of variables for functional differential equations, J. Differential Equations 18 (1975), 1-10.
  • [12] T. Kato, J.B. McLeod: The functional-differential equation y'(x) = ay(lambdax) + by(x), Bull. Amer. Math. Soc. 77 (1971), 891-937.
  • [13] T. Krisztin: A note on the convergence of the solutions of a linear functional-differential equation, J. Math. Anal. Appl. 145 (1990), 17-25.
  • [14] Y. Liu: Asymptotic behaviour of functional-differential equations with proportional time delays, Euro. J. Appl. Math. 7 (1996), 11-30.
  • [15] G. Makay, J. Terjeki: On the asymptotic behavior of the pantograph equations, Electron. J. Qual. Theory Differ. Equ. 2 (1998), 1-12.
  • [16] R.M. Mathsen, Q.R. Wang, H.W. Wu: Oscillation for neutral dynamic functional equations on time scales, J. Difference Equ. Appl. 10 (2004), 651-659.
  • [17] H. Peics: On the asymptotic behaviour of difference equations with continuous arguments, Ser. A. Math. Anal. 9 (2002), 257-273.
  • [18] B.G. Zhang, X. Deng: Oscillation of delay differential equations on time scales, Math. Comput. Modelling 36 (2002) 1307-1318.
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Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-AGH4-0007-0093
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