一阶时滞微分方程正周期解的存在性问题（英文）  

Positive Periodic Solutions of First-order Delay Differential Equations

作　　者：翁爱治[1] 

机构地区：[1]上海政法学院经济管理学院,上海201701

出　　处：《工程数学学报》2016年第1期106-110,共5页Chinese Journal of Engineering Mathematics

基　　金：The Committee of Science and Technology of Shanghai(13ZR1444500);the Shanghai University of Political Science and Law(sz12015)

摘　　要：本文研究一类一阶时滞微分方程正周期解的存在性问题,该类微分方程经线性化后可能是退化的.众所周知,大部分研究周期解存在性的方法都只适用于方程是非退化的情况.针对该问题,本文利用Schauder不动点定理给出周期解存在的定理.在文章的最后我们给出几个例子说明所获结论的正确性.In this paper, we study the existence of positive periodic solutions for a particular class of first-order delay differential equations, where the linearized system may be degenerate. It is known that most methods may fail to guarantee the existence of periodic solution under the degenerate case. To alleviate this issue, this paper presents an efficient Mgorithm based on Schauder＇s fixed point theorem. Theo- rems which list the conditions for the existence of periodic solutions are presented. Simulation studies show the correctness of the improved method.

关 键 词：正周期解 时滞微分方程 存在性 SCHAUDER不动点定理 

分 类 号：O175.14[理学—数学]