二阶多时滞微分方程周期解的存在性  

Existence of Periodic Solutions for Second Order Differential Equations with Multiple Delays

作　　者：朱俐玫 李永祥 ZHU Limei LI Yongxiang(College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Chin)

机构地区：[1]西北师范大学数学与统计学院,兰州730070

出　　处：《吉林大学学报（理学版）》2017年第5期1077-1083,共7页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:11261053;16611071);甘肃省自然科学基金(批准号:1208RJZA129)

摘　　要：利用上下解的单调迭代方法,考虑二阶多时滞微分方程-u″(t)=f(t,u(t),u(t-τ_1),u(t-τ_2),…,u(t-τ_n)),t∈Rω-周期解的存在性,其中:f:R×R^(n+1)→R连续,关于t以ω为周期;τ_1,τ_2,…,τ_n为正常数.通过建立新的极大值原理,构造方程ω-周期解的单调迭代求解程序,证明了ω-周期解的存在性与唯一性.Using the monotone iterative method of upper and lower solutions,we considered the existence ofω-periodic solutions for the second order differential equation with multiple delays -u″（t）=f（t,u（t）,u（t-τ1）,u（t-τ2）,…,u（t-τn））, t∈ R, where f：R×R^n＋1→R was a continuous function which wasω-periodic on t,and τ1,τ2,…,τn were positive constants.By establishing a new maximum principle,we constructed a monotone iterative procedure to seek theω-periodic solutions of the equation,and proved existence and uniqueness ofω-periodic solutions.

关 键 词：时滞微分方程 单调迭代方法 周期解 

分 类 号：O175.15[理学—数学] O177.91[理学—基础数学]