AIMS Mathematics, 2020, 5(6): 7372-7386. doi: 10.3934/math.2020472

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Positive periodic solution of first-order neutral differential equation with infinite distributed delay and applications

School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454000, China

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.
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