一类广义单种群Logistic模型正周期解的存在性和唯一性

数学物理学报 ›› 2009, Vol. 29 ›› Issue (5): 1442-1452.

一类广义单种群Logistic模型正周期解的存在性和唯一性

红河学院数学系云南蒙自 661100

收稿日期:2007-07-05 修回日期:2009-05-29 出版日期:2009-10-25 发布日期:2009-10-25
基金资助:
国家自然科学基金(10571062)、云南省教育厅科学研究基金(07Y10085)和红河学院博硕启动基金(XSS06009)资助

Existence and Uniqueness of Positive Periodic Solution for a Kind of Generalized Logistic Model of Single Species

Department of Mathematics, Honghe University, Yunnan Mengzi 661100

Received:2007-07-05 Revised:2009-05-29 Online:2009-10-25 Published:2009-10-25
Supported by:
国家自然科学基金(10571062)、云南省教育厅科学研究基金(07Y10085)和红河学院博硕启动基金(XSS06009)资助

摘要/Abstract

摘要：

该文利用Krasnoselskii不动点定理和Schwarz不等式, 获得了关于非自治的广义单种群Logistic模型
x=x(t){a(t)-b(t)x(t)-∑ⁿ_i₌₁c_i(t)x(t-τ_i(t))-∫⁰_-∞k(t, s)x(t+s)ds}

的正周期解的存在性和唯一性的一些新的结果.

关键词: 时滞微分方程, Krasnoselskii不动点定理, 周期解

Abstract:

By using the method of Krasnoselskii's fixed point theorem and Schwarz inequality, new results on the existence and uniqueness of positive ω-periodic solution for the nonautonomous generalized Logistic model of single species of the form

x=x(t){a(t)-b(t)x(t)-∑ⁿ_i=1c_i(t)x(t-τ_i(t))-∫⁰_-∞k(t, s)x(t+s)ds}
are obtained.

Key words: Delay differential equation, Uniqueness, Krasnoselskiis fixed point theorem, Periodic solutions

中图分类号:

34K13

杨鑫松, 芮伟国. 一类广义单种群Logistic模型正周期解的存在性和唯一性[J]. 数学物理学报, 2009, 29(5): 1442-1452.

YANG Xin-Song, RUI Wei-Guo. Existence and Uniqueness of Positive Periodic Solution for a Kind of Generalized Logistic Model of Single Species[J]. Acta mathematica scientia,Series A, 2009, 29(5): 1442-1452.

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