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We propose and analyze a mathematical model of hematopoietic stem cell dynamics. This model takes into account a finite number of stages in blood production, characterized by cell maturity levels, which enhance the difference, in the hematopoiesis process, between dividing cells that differentiate (by going to the next stage) and dividing cells that keep the same maturity level (by staying in the same stage). It is described by a system of n nonlinear differential equations with n delays. We study...

Asymptotic behavior of retarded differential equations.

Yeh, Cheh-Chih (1987)

International Journal of Mathematics and Mathematical Sciences

Asymptotic behaviour of a class of nonoscillatory solutions of differential equations with deviating arguments

Christos G. Philos (1983)

Mathematica Slovaca

Asymptotic behaviour of all solutions of differential systems with deviating arguments

Božena Mihalíková (1990)

Mathematica Slovaca

Asymptotic behaviour of solutions of linear differential equations with delay

Josef Diblík (1993)

Annales Polonici Mathematici

Inequalities for some positive solutions of the linear differential equation with delay ẋ(t) = -c(t)x(t-τ) are obtained. A connection with an auxiliary functional nondifferential equation is used.

Asymptotic formulas for solutions of the differential equation with advanced argument ${(x^{'} (t) / r (t))}^{'} + q (t) f (x (g (t))) = 0$

Miloš Ráb (1987)

Archivum Mathematicum

Asymptotic properties of solutions of differential systems with deviating argument

Božena Mihalíková (1989)

Czechoslovak Mathematical Journal

Asymptotic properties of solutions of functional differential systems

Anatolij F. Ivanov, Pavol Marušiak (1992)

Mathematica Bohemica

In the paper we study the existence of nonoscillatory solutions of the system $x_{i}^{(n)} (t) = \sum_{j = 1}^{2} p_{i j} (t) f_{i j} (x_{j} (h_{i j} (t))), n \geq 2, i = 1, 2$ , with the property $l i m_{t \to \infty} x_{i} (t) / t^{k_{i}} = c o n s t \neq 0$ for some $k_{i} \in {1, 2, ..., n - 1}, i = 1, 2$ . Sufficient conditions for the oscillation of solutions of the system are also proved.

Asymptotic properties of solutions of the $n$ th order differential equation with delayed argument

Marián Rusnák, Vincent Šoltés (1989)

Mathematica Slovaca

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