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Zbl 1061.34053
Lu, Shiping; Ge, Weigao
Existence of positive periodic solutions for neutral logarithmic population model with multiple delays.
(English)
[J] J. Comput. Appl. Math. 166, No. 2, 371-383 (2004). ISSN 0377-0427

The authors study the existence of positive periodic solutions for a neutral delay logarithmic population model with multiple delays of the form $${dN\over dt}= N(t)\Biggl[r(t)- \sum^N_{j=1} a_i(t)\ln N(t- \sigma_i(t))- \sum^m_{j=1} b_j(t){d\over dt}\ln N(t-\tau_j(t))\Biggr],\tag1$$ with $\sigma_j(t)\ge 0$ and $\tau_j(t)\ge 0$. The goal of this paper is to establish some criteria guaranteeing the existence of positive periodic solutions of (1). Under some suitable assumptions on the data of (1), the authors obtain a new existence result by using an abstract continuation theorem for $k$-set contraction and some other analytic techniques.
[Messoud A. Efendiev (Berlin)]
MSC 2000:
*34K13 Periodic solutions of functional differential equations
35K40 Systems of parabolic equations, general
34K60 Applications of functional-differential equations
92D25 Population dynamics

Keywords: neutral delay logarithmic population model; $k$-set contractive operator; positive periodic solution

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