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Zbl 1125.34055
Yuan, Rong
On almost periodic solutions of logistic delay differential equations with almost periodic time dependence.
(English)
[J] J. Math. Anal. Appl. 330, No. 2, 780-798 (2007). ISSN 0022-247X

The author studies an almost periodic delay differential equation of logistic type of the form $$N'(t)=N(t)[a(t)-b(t)f(N([t]))],$$ where $[\cdot]$ denotes the greatest integer function, $f(x)$ is continuously differentiable for $x>0$, $f(0)=0$, $f(x)>0$ for $x>0$, and $a(t)$ and $b(t)$ are positive almost periodic functions. Some criteria are established for the existence and module containment of almost periodic solutions. The study shows that not only the results due to George Seifert for the above equation with $b\equiv 1$ do hold for general $b$, but also the modules of almost periodic solutions can be characterized. The author also solves an open problem of G. Seifert.
[Meng Fan (Changchun)]
MSC 2000:
*34K14 Almost periodic solutions of functional differential equations

Keywords: logistic equations; delay; almost periodic solutions; module containment

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