n阶多时滞微分方程的周期解  

Periodic Solutions for nth Order Differential Equations with Multiple Delays

作　　者：李文金 庞彦尼[2] LI Wenjin;PANG Yanni(School of Applied Mathematics,Jilin University of Finance and Economics,Changchun 130117,China;College of Mathematics,Jilin University,Changchun 130012,China)

机构地区：[1]吉林财经大学应用数学学院,长春130117 [2]吉林大学数学学院,长春130012

出　　处：《吉林大学学报（理学版）》2021年第6期1351-1355,共5页Journal of Jilin University:Science Edition

基　　金：吉林省教育厅“十三五”科学技术研究规划项目(批准号:JJKH20200136KJ).

摘　　要：用上下解的单调迭代方法,通过建立新的极大值原理,构造n阶时滞微分方程-u^(n)(t)=f(t,u(t),u(t-τ1),u(t-τ2),…,u(t-τn)),t∈ℝω-周期解的单调迭代求解程序,并证明其ω-周期解的存在性和唯一性,其中f:ℝ×ℝ^(n+1)→ℝ连续且关于t以ω为周期,τ1,τ2,…,τn是正常数.By using the monotone iterative method of upper and lower solution and establishing a new maximum principle,we constructed a monotone iterative procedure for theω-periodic solutions of n th order delay differential equation-u^(n)(t)=f(t,u(t),u(t-τ1),u(t-τ2),…,u(t-τn)),t∈ℝ,and proved existence and uniqueness of itsω-periodic solutions,where f:ℝ×ℝ^(n+1)→ℝwas a continuous function which wasω-periodic on t,τ1,τ2,…,τn were positive constants.

关 键 词：时滞微分方程 周期解 极大值原理 

分 类 号：O175.14[理学—数学]