[1]韩飞,王全义.一类泛函微分方程周期正解的个数[J].华侨大学学报(自然科学版),2009,30(3):346-350.[doi:10.11830/ISSN.1000-5013.2009.03.0346]
　HAN Fei,WANG Quan-yi.Number of Positive Periodic Solutions for a Class of Functional Differential Equations[J].Journal of Huaqiao University(Natural Science),2009,30(3):346-350.[doi:10.11830/ISSN.1000-5013.2009.03.0346]
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一类泛函微分方程周期正解的个数()
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《华侨大学学报（自然科学版）》[ISSN:1000-5013/CN:35-1079/N]

卷:
第30卷
期数:
2009年第3期
页码:
346-350
栏目:
出版日期:
2009-05-20

文章信息/Info

Title:
Number of Positive Periodic Solutions for a Class of Functional Differential Equations
文章编号:
1000-5013(2009)03-0346-05
作者:
韩飞; 王全义
华侨大学数学科学学院
Author(s):
HAN Fei;  WANG Quan-yi
School of Mathematics Sciences, Huaqiao University, Quanzhou 362021, China
关键词:
不动点定理;  锥;  周期正解;  泛函微分方程
Keywords:
fixed point theorem;  cone;  positive periodic solution;  functional differential equation
分类号:
O175.14
DOI:
10.11830/ISSN.1000-5013.2009.03.0346
文献标志码:
A
摘要:
研究一类带有一个参数的非线性泛函微分方程x′(t)=a(t,x(t))x(t)-λb(t)f(x(t-τ(t)))的周期正解的个数问题.利用锥压缩锥拉伸不动点定理,解决该类方程周期正解的存在问题.给出根据参数判断该类方程存在1个、2个,以及不存在周期正解的充分条件.结果表明,这些充分性条件简单,容易验证.
Abstract:
In this paper,we study a class of non-linear functional differential equations with one parameter.By employing the cone compression and extension fixed point theorem,we solve the existence of positive periodic solutions for this class of equations.Some sufficient conditions which determine the existence of one or two positive solutions and nonexistence of positive periodic solutions for the equation are presented.These conditions are simple and easily verifiable.

参考文献/References:

[1] WANG Hai-yan. Positive periodic solutions of functional differential equations [J]. Journal of Differential Equations, 2004, (2):354-366.doi:10.1016/j.jde.2004.02.018.
[2] KUANG Y, SMITH H L. Periodic solutions of differential delay equations related to threshold-type delays, oscil lations and dynamics in delay equations [J]. Contemporary Mathematics, 1992.153-176.
[3] LI Y K. Periodic solutions of periodic delay Lotka-Volterra equation and systems [J]. Journal of Mathematical Analysis and Applications, 2001, (1):260-280.doi:10.1006/jmaa.2000.7248.
[4] 韩 飞, 王全义. 具状态依赖时滞微分方程的周期正解 [J]. 华侨大学学报(自然科学版), 2005(4):357-360.
[5] 郭大均. 非线性泛函分析 [M]. 济南:山东科学技术出版社, 2003.286-330.

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备注/Memo

备注/Memo:
福建省自然科学基金资助项目(Z0511026); 国务院侨办科研基金资助项目(07QZR09)
更新日期/Last Update: 2014-03-23