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Zbl 1147.92031
Li, Jingwen; Du, Chaoxiong
Existence of positive periodic solutions for a generalized Nicholson's blowflies model. (English)
[J] J. Comput. Appl. Math. 221, No. 1, 226-233 (2008). ISSN 0377-0427

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 {\it A. J. Nicholson}'s [An outline of the dynamics of animal populations. Aust. J. Zool. 2, 9--25 (1954)] blowflies model: $$x'(t)=- \delta(t)x(t)+ \sum_{i=1}^m p_i(t)x(t-\tau_i(t)) e^{-q_i(t)x(t-\tau_i(t))}, \quad t\ge 0.$$ 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.

MSC 2000:: *92D25 Population dynamics
34K13 Periodic solutions of functional differential equations
34K60 Applications of functional-differential equations

Keywords: cone fixed point theorem

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