Positive Periodic Solutions for a Single-species Model with Delay Weak Kernel and Cycle Mortality

In this paper, by using the Krasnoselskii''s fixed-point theorem, we study the existence of positive periodic solutions of the following single-species model with delay weak kernel and cycle mortality:begin{align*}x''(t) = rx(t) Big[1-frac{1}{K}int_{-infty}^{t}alpha e^{-alpha(t-s)}x(s)dsBig] -a(t)x(t),end{align*}and get the necessary conditions for the existence of positive periodic solutions. Finally, an example and numerical simulation are used to illustrate the validity of our results.