Electron. J. Diff. Eqns., Vol. 2007(2007), No. 13, pp. 1-10.

Positive periodic solutions of neutral logistic equations with distributed delays

Yongkun Li, Guoqiao Wang, Huimei Wang

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,
$$ x'(t)= x(t)\Big[a(t)-\sum_{i=1}^n a_i(t)\int_{-T_i}^0 x(t+\theta)\, d\mu_i(\theta)- \sum_{j=1}^m b_j(t) \int_{-\hat{T}_j}^0 x'(t+\theta)\,d\nu_j(\theta)\Big], $$
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 $\int_{-T_i}^0\,d \mu_i=1$ and $\int_{-\hat{T}_j}^0\,d \nu_j=1$.

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.

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Yongkun Li
Department of Mathematics, Yunnan University
Kunming, Yunnan 650091, China
email: yklie@ynu.edu.cn
Guoqiao Wang
Department of Mathematics, Yunnan University
Kunming, Yunnan 650091, China
email:wgq81@126.com
Huimei Wang
Department of Mathematics, Yunnan University
Kunming, Yunnan 650091, China
email: wanghmei@163.com

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