*(English)*Zbl 1048.34114

The author considers the following nonlinear delay differential equation

where $k$ is a positive integer, $\beta \left(t\right)$ and $\gamma \left(t\right)$ are positive periodic functions of period $\omega $. The main result for the nondelay case is Theorem 2.1, where the author proves that (1) has a unique positive periodic solution $\overline{p}\left(t\right)$. He also studies the global attractivity of $\overline{p}\left(t\right)$. In the delay case, sufficient conditions for the oscillation of all positive solutions to (1) about $\overline{p}\left(t\right)$ are given, also some sufficient conditions for the global attractivity of $\overline{p}\left(t\right)$ are established. It should be noted that (1) is a modification of an equation proposed as a model of hematopoiesis. Similar equations are also used as models in population dynamics.