Summary: 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 A. J. Nicholson’s [An outline of the dynamics of animal populations. Aust. J. Zool. 2, 9–25 (1954)] blowflies model:
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.