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.