| 一类具分布时滞的微分方程的正周期解的存在性与多解性 |
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| 引用本文： | 秦发金,姚晓洁.一类具分布时滞的微分方程的正周期解的存在性与多解性[J].数学的实践与认识,2007,37(1):133-140. |
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| 作者姓名： | 秦发金 姚晓洁 |
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| 作者单位： | 广西柳州师范高等专科学校数计系,柳州,545004 |
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| 摘 要： | 讨论具分布时滞的微分方程x′(t)=-a(t,x)x(t)+∫-0τf(t,r,x(t+r))dr,x′(t)=a(t,x)x(t)-∫0-τf(t,r,x(t+r))drx′(t)=-g(t,x(t))+∫0-τf(t,r,x(t+r))dr,x′(t)=g(t,x(t))-∫0-τf(t,r,x(t+r))dr正周期解问题,利用锥不动点定理,获得了这类问题正解存在性和多重性的充分条件,推广了已有文献的相关结果.
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| 关 键 词： | 分布时滞 正周期解 锥不动点定理 存在性 多解性 |
| 修稿时间： | 2006年6月27日 |
Existence and Multiplicity of Positive Periodic Solutions for A Class of Differential Equation with Distributed Delay |
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| QIN Fa-jin,YAO Xiao-jie.Existence and Multiplicity of Positive Periodic Solutions for A Class of Differential Equation with Distributed Delay[J].Mathematics in Practice and Theory,2007,37(1):133-140. |
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| Authors: | QIN Fa-jin YAO Xiao-jie |
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| Abstract: | The positive periodic solutions is discussed for a class of differential equation with distributed delayx′(t)=-a(t,x)x(t)+∫~0_(-τ)f(t,r,x(t+r))dr,x′(t)=a(t,x)x(t)-∫~0_(-τ)f(t,r,x(t+r))drx′(t)=-g(t,x(t))+∫~0_(-τ)f(t,r,x(t+r))dr,x′(t)=g(t,x(t))-∫~0_(-τ)f(t,r,x(t+r))drSome sufficient conditions for the existence and multiplicity solutions of positive periodic solutions were obtained by using the fixed-point theorem.The results have extend and improved the related reports in the literatures. |
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| Keywords: | distributed delay positive periodic solutions fixed point theorem existence multiplicity solutions |
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