n阶多时滞微分方程的周期解

Periodic Solutions for nth Order Differential Equations with Multiple Delays

用上下解的单调迭代方法,通过建立新的极大值原理,构造n阶时滞微分方程-u^(n)(t)=f(t,u(t),u(t-τ1),u(t-τ2),…,u(t-τn)),t∈ℝω-周期解的单调迭代求解程序,并证明其ω-周期解的存在性和唯一性,其中f:ℝ×ℝ^(n+1)→ℝ连续且关于t以ω为周期,τ1,τ2,…,τn是正常数.

By using the monotone iterative method of upper and lower solution and establishing a new maximum principle,we constructed a monotone iterative procedure for theω-periodic solutions of n th order delay differential equation-u^(n)(t)=f(t,u(t),u(t-τ1),u(t-τ2),…,u(t-τn)),t∈ℝ,and proved existence and uniqueness of itsω-periodic solutions,where f:ℝ×ℝ^(n+1)→ℝwas a continuous function which wasω-periodic on t,τ1,τ2,…,τn were positive constants.