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

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.