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Zbl 1186.34116
Alzabut, J.O.; Nieto, J.J.; Stamov, G.Tr.
Existence and exponential stability of positive almost periodic solutions for a model of hematopoiesis. (English)
[J] Bound. Value Probl. 2009, Article ID 127510, 10 p. (2009). ISSN 1687-2770/e

The authors consider the following hematopoiesis equation with impulses $$\cases h^{\prime}(t)=-\alpha(t)h(t)+\frac{\beta(t)}{1+h^n(t-\tau)},&t\not=\theta_k,\\ \Delta(\theta_k):=h(\theta_k^+)-h(\theta_k^-)=\gamma_kh(\theta_k^-)+\delta_k,&k\in \mathbb{N}. \endcases\tag1$$ Sufficient conditions for the existence of a positive almost periodic solution $p(t)$ and its exponential stability are obtained.
[Peixuan Weng (Guangzhou)]

MSC 2000:: *34K60 Applications of functional-differential equations
34K45 Equations with impulses
34K14 Almost periodic solutions of functional differential equations
34K20 Stability theory of functional-differential equations

Keywords: model of hematopoiesis; differential equation with impulse; positive almost periodic solution; exponential stability

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