高阶多时滞微分方程周期解的存在性  

Existence of Periodic Solutions for Higher-Order Differential Equations with Multiple Delays

作　　者：章欢 李永祥 ZHANG Huan;LI Yongxiang(College of Mathematics and Statistics,Northwest Normal University ,Lanzhou 730070,China)

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）》2018年第6期1291-1298,共8页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:11261053;11661071)

摘　　要：利用上下解的单调迭代方法,考虑n阶多时滞微分方程u(n)(t)+a(t)u(t)=f(t,u(t-τ_1),u(t-τ_2),…,u(t-τ——k)),t∈Rω-周期解的存在性,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,得到了该方程ω-周期解的存在性与唯一性结果.其中:n≥2;a:R→(0,∞)连续,以ω为周期;f:R×Rk→R连续,关于t以ω为周期;τ1,τ2,…,τk≥0为常数.Using the monotone iterative method of upper and lowersolutions,we considered the existence ofω-periodic solutions for the nth-order differential equation with multiple delaysu^(n)(t)+a(t)u(t)=f(t,u(t-τ1),u(t-τ2),…,u(t-τk)), t∈R.By establishing a new maximum principle,weconstructed a monotone iterative procedure for solving theω-periodic solutions of the equation,and obtained the existence and uniqueness results ofω-periodic solutions of the equation.Where n≥2,a:R→(0,∞)is acontinuous function which isω-periodic,f:R×R^k→R is a continuous function which isω-periodic on t,andτ1,τ2,…,τk≥0 are constants.

关 键 词：时滞微分方程 上下解 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]