Existence of positive periodic solutions for a generalized Nicholson’s blowflies model

In this paper, by using the Krasnoselskii cone fixed point theorem, we obtain a sufficient condition as well as a necessary condition for the existence of positive periodic solutions of the following generalized Nicholson’s blowflies model: x′(t)=−δ(t)x(t)+∑i=1mpi(t)x(t−τi(t))e−qi(t)x(t−τi(t)),t≥0. In the degenerate case, i.e., where the coefficients and delays of the above equation are all constants, a sufficient and necessary condition for the existence of positive periodic solutions is obtained. Our results are completely new, and generalize and improve some results from the literature.