In this paper, we consider first-order neutral differential equation with infinite distributed delay, where nonlinear term may satisfy sub-linearity, semi-linearity and super-linearity conditions. By virtue of a fixed point theorem of Leray-Schauder type, we prove the existence of positive periodic solutions. As applications, we prove that Hematopoiesis model, Nicholson’s blowflies model and the model of blood cell production have positive periodic solutions.

中文翻译：

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具有无限分布时滞的一阶中立型微分方程的正周期解及其应用

在本文中，我们考虑具有无限分布延迟的一阶中立型微分方程，其中非线性项可以满足亚线性，半线性和超线性条件。借助于Leray-Schauder型不动点定理，我们证明了正周期解的存在。作为应用，我们证明了造血模型，尼科尔森的蝇s模型和血细胞产生模型具有正周期解。