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Existence of positive periodic solutions for neutral logarithmic population model with multiple delays. (English) Zbl 1061.34053
The authors study the existence of positive periodic solutions for a neutral delay logarithmic population model with multiple delays of the form ${dN\over dt}= N(t)\Biggl[r(t)- \sum^N_{j=1} a_i(t)\ln N(t- \sigma_i(t))- \sum^m_{j=1} b_j(t){d\over dt}\ln N(t-\tau_j(t))\Biggr],\tag{1}$ with $$\sigma_j(t)\geq 0$$ and $$\tau_j(t)\geq 0$$. 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.

##### MSC:
 34K13 Periodic solutions to functional-differential equations 35K40 Second-order parabolic systems 34K60 Qualitative investigation and simulation of models involving functional-differential equations 92D25 Population dynamics (general)
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##### References:
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