# zbMATH — the first resource for mathematics

##### Examples
 Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. "Topological group" Phrases (multi-words) should be set in "straight quotation marks". au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted. Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff. "Quasi* map*" py: 1989 The resulting documents have publication year 1989. so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14. "Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic. dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles. py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses). la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

##### Operators
 a & b logic and a | b logic or !ab logic not abc* right wildcard "ab c" phrase (ab c) parentheses
##### Fields
 any anywhere an internal document identifier au author, editor ai internal author identifier ti title la language so source ab review, abstract py publication year rv reviewer cc MSC code ut uncontrolled term dt document type (j: journal article; b: book; a: book article)
Oscillation and global attractivity in hematopoiesis model with periodic coefficients. (English) Zbl 1048.34114

The author considers the following nonlinear delay differential equation

${p}^{\text{'}}\left(t\right)=\frac{\beta \left(t\right){p}^{m}\left(t-k\omega \right)}{1+{p}^{n}\left(t-k\omega \right)}-\gamma \left(t\right)p\left(t\right),\phantom{\rule{2.em}{0ex}}\left(1\right)$

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.

##### MSC:
 34K11 Oscillation theory of functional-differential equations 34K20 Stability theory of functional-differential equations 92D25 Population dynamics (general) 92C50 Medical applications of mathematical biology 34K60 Qualitative investigation and simulation of models
##### Keywords:
oscillation; global attractivity; hematopoiesis