有序Banach空间中二阶时滞微分方程正周期解的存在性

Existence of Positive Periodic Solution for Second Order Differential Equation with Delays in Ordered Banach Spaces

研究了有序Banach空间E中二阶多时滞微分方程-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∈C(R)是正的ω-周期函数;f:R×Kn→K连续且f(t,v)关于t为ω-周期函数;v=(ν_1,ν_2,…,νn)∈K^n;K为正元锥;τ_i≥0,i=1,2,…n为常数.在较一般的非紧性测度条件与有序条件下,应用凝聚映射的不动点指数理论,获得了该问题正ω-周期解的存在性结果.

Existence of positiveω-periodic solution was studied for second order differential equation with delays in ordered Banach space E-u″（t） ＋a（t）u（t） =f（t,u（t-τ1）,…,u（t-τn））,t∈R, where a∈C（ R） was a positive ω-periodic function,f：R ×Kn→K was a continuous function, and f（ t,v） wasω-periodic in t, v=（ν1,ν2,…,νn）∈Kn, K was the positive cone,τi≥0,i=1,2,…n were constants. Un-der more general conditions of noncompactness measure and semi-ordering, the existence results of posi-tive ω-periodic solutions were obtained by applying the fixed point fixed theory of condensing mapping.