Asymptotic estimation for functional differential equations with several delays

Jan Čermák

Archivum Mathematicum (1999)

  • Volume: 035, Issue: 4, page 337-345
  • ISSN: 0044-8753

Abstract

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We discuss the asymptotic behaviour of all solutions of the functional differential equation y ' ( x ) = ∑ i = 1 m a i ( x ) y ( τ i ( x ) ) + b ( x ) y ( x ) , where b ( x ) < 0 . The asymptotic bounds are given in terms of a solution of the functional nondifferential equation ∑ i = 1 m | a i ( x ) | ω ( τ i ( x ) ) + b ( x ) ω ( x ) = 0 .

How to cite

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Čermák, Jan. "Asymptotic estimation for functional differential equations with several delays." Archivum Mathematicum 035.4 (1999): 337-345. <http://eudml.org/doc/248360>.

@article{Čermák1999,
abstract = {We discuss the asymptotic behaviour of all solutions of the functional differential equation \[y^\{\prime \}(x)=\sum \_\{i=1\}^ma\_i(x)y(\tau \_i(x))+b(x)y(x)\,,\] where $b(x)<0$. The asymptotic bounds are given in terms of a solution of the functional nondifferential equation \[\sum \_\{i=1\}^m|a\_i(x)|\omega (\tau \_i(x))+b(x)\omega (x)=0.\]},
author = {Čermák, Jan},
journal = {Archivum Mathematicum},
keywords = {functional differential equation; functional nondifferential equation; asymptotic behaviour; transformation; functional differential equation; functional nondifferential equation; asymptotic behaviour; transformation},
language = {eng},
number = {4},
pages = {337-345},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Asymptotic estimation for functional differential equations with several delays},
url = {http://eudml.org/doc/248360},
volume = {035},
year = {1999},
}

TY - JOUR
AU - Čermák, Jan
TI - Asymptotic estimation for functional differential equations with several delays
JO - Archivum Mathematicum
PY - 1999
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 035
IS - 4
SP - 337
EP - 345
AB - We discuss the asymptotic behaviour of all solutions of the functional differential equation \[y^{\prime }(x)=\sum _{i=1}^ma_i(x)y(\tau _i(x))+b(x)y(x)\,,\] where $b(x)<0$. The asymptotic bounds are given in terms of a solution of the functional nondifferential equation \[\sum _{i=1}^m|a_i(x)|\omega (\tau _i(x))+b(x)\omega (x)=0.\]
LA - eng
KW - functional differential equation; functional nondifferential equation; asymptotic behaviour; transformation; functional differential equation; functional nondifferential equation; asymptotic behaviour; transformation
UR - http://eudml.org/doc/248360
ER -

References

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  1. On the asymptotic behaviour of solutions of certain functional differential equations, Math. Slovaca 48 (1998), 187–212. (1998) MR1647674
  2. The asymptotic bounds of linear delay systems, J. Math. Anal. Appl. 225 (1998), 373–388. (1998) MR1644331
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  4. Introduction to Functional Differential Equations, Springer-Verlag, New York, 1993. (1993) MR1243878
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  6. The functional differential equation y ' ( x ) = a y ( λ x ) + b y ( x ) , Bull. Amer. Math. Soc. 77 (1971), 891–397. (1971) MR0283338
  7. Iterative Functional Equations, Encyclopedia of Mathematics and its Applications, Cambridge University Press, 1990. (1990) MR1067720
  8. Simultaneous solutions of a system of Abel equations and differential equations with several deviations, Czechoslovak Math. J. 32 (107) (1982), 488–494. (1982) Zbl0524.34070MR0669790
  9. Transformations and canonical forms of functional-differential equations, Proc. Roy. Soc. Edinburgh 115A (1990), 349–357. (1990) MR1069527
  10. On Simultaneous Abel equations, Aequationes Math. (1989), 163–177. (1989) Zbl0686.39009MR1018910

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