一类三阶时滞微分方程在Banach空间中的周期解的存在性  

Existence of periodic solutions of a class of third order delay differential equations in Banach spaces

作　　者：陈雨佳 杨和 CHEN Yu-jia;YANG He(College of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070,Gansu,Chin)

机构地区：[1]西北师范大学数学与统计学院,甘肃兰州730070

出　　处：《山东大学学报（理学版）》2018年第8期84-94,共11页Journal of Shandong University(Natural Science)

基　　金：国家基金委青年基金科学资助项目(11701457);甘肃省科技计划资助项目(17JR5RA071)

摘　　要：利用上下解单调迭代方法,考虑有序Banach空间E中三阶时滞微分方程u″′(t)+M_0u(t-τ_0)=f(t,u(t),u(t-τ_1),u(t-τ_2)),t∈R,2π-周期解的存在性,其中f:R×E^3→E连续,关于t以2π-为周期,τ_0,τ_1,τ_2为正常数。通过建立新的极大值原理和构造方程2π-周期解的单调迭代求解程序,得到了该方程2π-周期解的存在性与唯一性结果。Applying the monotone iterative method of upper and lower solutions,we discuss the existence of 2π-periodic solutions for the third-order differential equation with delays in ordered Banach space Eu″′（ t） ＋ M0u（ t-τ0）= f（ t,u（ t）,u（ t-τ1）,u（ t-τ2））, t∈R,where f：R × E3→E is a continuous function which is 2π-periodic in t,and τ0,τ1,τ2 are positive constants. By establishing a new maximum principle,a monotone iterative procedure for the equation is constructed. Some existence and uniqueness results of 2π-periodic solutions for this equation are obtained.

关 键 词：有序BANACH空间 极大值原理 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]