On the delay differential equation y'(x) = ay(τ(x)) + by(x)

Jan Čermák. "On the delay differential equation y'(x) = ay(τ(x)) + by(x)." Annales Polonici Mathematici 71.2 (1999): 161-169. <http://eudml.org/doc/262656>.

@article{JanČermák1999,
abstract = {The paper discusses the asymptotic properties of solutions of the scalar functional differential equation $y^\{\prime \}(x) = ay(τ(x)) + by(x), x ∈ [x_0,∞]$. Asymptotic formulas are given in terms of solutions of the appropriate scalar functional nondifferential equation.},
author = {Jan Čermák},
journal = {Annales Polonici Mathematici},
keywords = {functional differential equation; functional (nondifferential) equation; asymptotic behaviour; 39B05; scalar linear functional-differential equation; asymptotic characterization; solutions},
language = {eng},
number = {2},
pages = {161-169},
title = {On the delay differential equation y'(x) = ay(τ(x)) + by(x)},
url = {http://eudml.org/doc/262656},
volume = {71},
year = {1999},
}

TY - JOUR
AU - Jan Čermák
TI - On the delay differential equation y'(x) = ay(τ(x)) + by(x)
JO - Annales Polonici Mathematici
PY - 1999
VL - 71
IS - 2
SP - 161
EP - 169
AB - The paper discusses the asymptotic properties of solutions of the scalar functional differential equation $y^{\prime }(x) = ay(τ(x)) + by(x), x ∈ [x_0,∞]$. Asymptotic formulas are given in terms of solutions of the appropriate scalar functional nondifferential equation.
LA - eng
KW - functional differential equation; functional (nondifferential) equation; asymptotic behaviour; 39B05; scalar linear functional-differential equation; asymptotic characterization; solutions
UR - http://eudml.org/doc/262656
ER -

References

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[1] N. G. de Bruijn, The difference-differential equation $F^{'} (x) = e^{α x + β} F (x - 1)$ , I, II, Nederl. Akad. Wettensch. Proc. Ser. A 56 = Indag. Math. 15 (1953), 449-464.
[2] J. Diblík, Asymptotic behaviour of solutions of linear differential equations with delay, Ann. Polon. Math. 58 (1993), 131-137. Zbl0784.34053
[3] J. Diblík, Asymptotic representation of solutions of equation ẏ(t) = β(t)[y(t)-y(t-τ(t))], J. Math. Anal. Appl. 217 (1998), 200-215. Zbl0892.34067
[4] I. Győri and M. Pituk, Comparison theorems and asymptotic equilibrium for delay differential and difference equations, Dynam. Systems Appl. 5 (1996), 277-302. Zbl0859.34053
[5] M. L. Heard, A change of variables for functional differential equations, J. Differential Equations 18 (1975), 1-10.
[6] T. Kato and J. B. McLeod, The functional differential equation y'(x) = ay(λx) + by(x), Bull. Amer. Math. Soc. 77 (1971), 891-937. Zbl0236.34064
[7] M. Kuczma, B. Choczewski and R. Ger, Iterative Functional Equations, Encyclopedia Math. Appl., Cambridge Univ. Press, 1990.
[8] F. Neuman, On transformations of differential equations and systems with deviating argument, Czechoslovak Math. J. 31 (1981), 87-90. Zbl0463.34051
[9] M. Pituk, On the limits of solutions of functional differential equations, Math. Bohemica 118 (1993), 53-66.

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