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  

Existence and Multiplicity of Positive Periodic Solutions for A Class of Differential Equation with Distributed Delay

作　　者：秦发金[1] 姚晓洁[1] 

机构地区：[1]广西柳州师范高等专科学校数计系,柳州545004

出　　处：《数学的实践与认识》2007年第1期133-140,共8页Mathematics in Practice and Theory

基　　金：国家自然科学基金(10571008)

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.The positive periodic solutions is discussed for a class of differential equation with distributed delay x＇（t）=-a（t,x）x（t）＋∫-t^0f（t,r,x（t＋r））dr,x＇（t）=a（t,x）x（t）-∫-t^0f（t,r,x（t＋r））dr x＇（t）=-g（t,x）x（t）＋∫-t^0f（t,r,x（t＋r））dr,x＇（t）=g（t,x）x（t）-∫-t^0f（t,r,x（t＋r））dr Some 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.

关 键 词：分布时滞 正周期解 锥不动点定理 存在性 多解性 

分 类 号：O175[理学—数学]