一类泛函微分方程半正问题的正周期解

莫宜春,孙晋易,王珍燕

(西北师范大学数学与信息科学学院,甘肃 兰州 730070)

一类泛函微分方程半正问题的正周期解

莫宜春,孙晋易,王珍燕

(西北师范大学数学与信息科学学院,甘肃 兰州 730070)

运用Krasnosel′skii不动点理论研究了一类含参泛函微分方程半正问题正周期解的存在性,获得了当参数充分小时正周期解的存在性结果以及半正问题正周期解存在的充分条件.丰富了一阶泛函微分方程解的存在性理论.

泛函微分方程;不动点定理;正周期解;存在性

1 引言及主要结果

带有周期时滞的泛函微分方程在生物学、经济学、生态学和人口动力系统等实际问题中有着广泛的应用,例如动物血红细胞存在模型,人口动力系统模型等.因此,对带有周期时滞的泛函微分方程周期解存在性的研究就更具有现实意义.近年来,许多学者对泛函微分方程周期解的存在性进行了深入而细致的研究,并取得了相当丰富的研究成果[18].

正周期解的存在性.显然,文献[7-8]中要求非线性项f是非负的.当然,很自然的问题是:非线性项f允许取负值时,方程(1.1)是否仍然存在正周期解?据笔者所知,此问题还没有被讨论过.鉴于此,本文试图回答此问题.本文的研究将会进一步丰富一阶泛函微分方程(1.1)解的存在性理论.

本文总假定:

2 预备知识

3 主要结果的证明

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A positive periodic solutions for semipositone problems of functional di ff erential equations

Mo Yichun,Sun Jinyi,Wang Zhenyan
(College of Mathematics and Information Science,Northwest Normal University,Lanzhou 730070,China)

By using Krasnosel'skii fi xed-point theorem in cones,this paper studies the existence of positive periodic solutions for semipositone problems of functional di ff erential equations.We obtain the existence of positive periodic solutions when the parameter is small enough,and the sufficient conditions for existence of positive periodic solutions for semipositone problems,enriching the theory for existence of solutions of functional di ff erential equations.

functional di ff erential equations, fi xed-point theorem,positive periodic solutions,existence

O178

A

1008-5513(2012)01-0137-06

2011-03-18.

国家自然科学基金(10671158);甘肃省自然科学基金(3ZS051-A25-016);NWNU-KJCXGC-03-17;春辉计划(Z2004-1-62033);高等学校博士学科点专项基金(20060736001);教育部留学回国人员启动资金(2006[311]).

莫宜春(1987-),硕士,研究方向：常微分方程边值问题.

2010 MSC:15A42