Asymptotic behaviour of solutions of some linear delay differential equations

Jan Čermák

Mathematica Bohemica (2000)

  • Volume: 125, Issue: 3, page 355-364
  • ISSN: 0862-7959

Abstract

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In this paper we investigate the asymptotic properties of all solutions of the delay differential equation y’(x)=a(x)y((x))+b(x)y(x),      xI=[x0,). We set up conditions under which every solution of this equation can be represented in terms of a solution of the differential equation z’(x)=b(x)z(x),      xI and a solution of the functional equation |a(x)|((x))=|b(x)|(x),      xI.

How to cite

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Čermák, Jan. "Asymptotic behaviour of solutions of some linear delay differential equations." Mathematica Bohemica 125.3 (2000): 355-364. <http://eudml.org/doc/248684>.

@article{Čermák2000,
abstract = {In this paper we investigate the asymptotic properties of all solutions of the delay differential equation y’(x)=a(x)y((x))+b(x)y(x),      xI=[x0,). We set up conditions under which every solution of this equation can be represented in terms of a solution of the differential equation z’(x)=b(x)z(x),      xI and a solution of the functional equation |a(x)|((x))=|b(x)|(x),      xI.},
author = {Čermák, Jan},
journal = {Mathematica Bohemica},
keywords = {asymptotic behaviour; differential equation; delayed argument; functional equation; asymptotic behaviour; differential equation; delayed argument; functional equation},
language = {eng},
number = {3},
pages = {355-364},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Asymptotic behaviour of solutions of some linear delay differential equations},
url = {http://eudml.org/doc/248684},
volume = {125},
year = {2000},
}

TY - JOUR
AU - Čermák, Jan
TI - Asymptotic behaviour of solutions of some linear delay differential equations
JO - Mathematica Bohemica
PY - 2000
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 125
IS - 3
SP - 355
EP - 364
AB - In this paper we investigate the asymptotic properties of all solutions of the delay differential equation y’(x)=a(x)y((x))+b(x)y(x),      xI=[x0,). We set up conditions under which every solution of this equation can be represented in terms of a solution of the differential equation z’(x)=b(x)z(x),      xI and a solution of the functional equation |a(x)|((x))=|b(x)|(x),      xI.
LA - eng
KW - asymptotic behaviour; differential equation; delayed argument; functional equation; asymptotic behaviour; differential equation; delayed argument; functional equation
UR - http://eudml.org/doc/248684
ER -

References

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  9. T. Kato J. B. McLeod, [unknown], Bull. Amer. Math. Soc. 77 (1971), 891-937. (1971) MR0283338
  10. M. Kuczma B. Choczewski R. Ger, Iterative Functional Equations, Encyclopedia of Mathematics and Its Applications, Cambridge Univ. Press, Cambridge, England, 1990. (1990) MR1067720
  11. F. Neuman, On transformations of differential equations and systems with deviating argument, Czechoslovak Math, J. 31 (1981), 87-90. (1981) Zbl0463.34051MR0604115
  12. S. N. Zhang, Asymptotic behaviour and structure of solutions for equation x ˙ ( t ) = p ( t ) [ x ( t ) - x ( t - 1 ) ] , J. Anhui Normal Univ. Nat. Sci. 2 (1981), 11-21. (In Chinese.) (1981) 

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