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

Annales Polonici Mathematici (1999)

- Volume: 71, Issue: 2, page 161-169
- ISSN: 0066-2216

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topJan 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

top- [1] N. G. de Bruijn, The difference-differential equation ${F}^{\text{'}}\left(x\right)={e}^{\alpha x+\beta}F(x-1)$, 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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