有序Banach空间二阶时滞微分方程的正周期解  

Positive periodic solutions for the second order differential equation with delays in ordered Banach spaces

作　　者：李玉玉[1] 

机构地区：[1]甘肃交通职业技术学院,甘肃兰州730070

出　　处：《西北师范大学学报（自然科学版）》2017年第1期5-11,共7页Journal of Northwest Normal University(Natural Science)

基　　金：国家自然科学基金资助项目(11561603);甘肃交通职业技术学院资助项目(2015Y-06)

摘　　要：讨论有序Banach空间E中二阶时滞微分方程-u″(t)+a(t)u(t)=f(t,u(t-τ_1),…,u(t-τ_n)),t∈R正ω-周期解的存在性,其中a是定义在实数空间R上正的连续的ω-周期函数,f:R×E^n→E连续,且关于t以ω为周期,τ_1,τ_2,…,τ_n>0为常数.在较一般的非紧性测度条件与序条件下用凝聚映射的不动点指数理论获得了该问题正周期解的存在性结果.The existence of positive periodic solutions for the second-order differential equation with multiple delays -u″（t）＋a（t）u（t）=f（t,u（t-τ1）,…,u（t-τn））,t∈R is discussed in an order Banach spaces E, where α∈C（R） is a positive w-periodic function and ,f：R×E^n→Eis a continuous function which is ~o-periodic in t, τ1,τ2,…,τn are positive constants. Under moregeneral conditions of noncompactness and semi-ordering, the existence result of positive periodic solutions is obtained by employing the fixed point index theory of condensing mapping.

关 键 词：Banach空间时滞微分方程 闭凸锥 凝聚映射 不动点指数 正周期解 

分 类 号：O175.15[理学—数学]