Electronic Journal of Differential Equations,
Vol. 2007(2007), No. 13, pp. 1-10.

Title: Positive periodic solutions of  neutral
       logistic equations with distributed delays

Authors: Yongkun Li   (Yunnan Univ., Kunming, China)
         Guoqiao Wang (Yunnan Univ., Kunming, China)
	 Huimei Wang  (Yunnan Univ., Kunming, China)

Abstract:
 Using a fixed point theorem of strict-set-contraction,
 we establish criteria for the existence of positive periodic
 solutions for the periodic neutral logistic equation,
 with distributed delays,
 $$
 x'(t)= x(t)\Big[a(t)-\sum_{i=1}^n a_i(t)\int_{-T_i}^0  x(t+\theta)\,
 \mathrm{d}\mu_i(\theta)- \sum_{j=1}^m b_j(t)
 \int_{-\hat{T}_j}^0 x'(t+\theta)\,\mathrm{d}\nu_j(\theta)\Big],
 $$
 where the coefficients $a, a_i ,b_j$ are continuous and periodic functions,
 with the same period. The values $T_i, \hat{T}_j$ are positive,
 and the functions  $\mu_i, \nu_j$   are nondecreasing   with
 $\int_{-T_i}^0\,{\rm d} \mu_i=1$ and
 $\int_{-\hat{T}_j}^0\,{\rm d} \nu_j=1$.
 
Submitted July 14, 2006. Published January 8, 2007.
Math Subject Classifications: 34K13, 34K40.
Key Words: Positive periodic solution;  neutral delay logistic equation;
           strict-set-contraction.