二阶多时滞微分方程周期解的存在性

Existence of Periodic Solutions for Second Order Differential Equations with Multiple Delays

利用上下解的单调迭代方法,考虑二阶多时滞微分方程-u″(t)=f(t,u(t),u(t-τ_1),u(t-τ_2),…,u(t-τ_n)),t∈Rω-周期解的存在性,其中:f:R×R^(n+1)→R连续,关于t以ω为周期;τ_1,τ_2,…,τ_n为正常数.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,证明了ω-周期解的存在性与唯一性.

Using the monotone iterative method of upper and lower solutions,we considered the existence ofω-periodic solutions for the second order differential equation with multiple delays -u″（t）=f（t,u（t）,u（t-τ1）,u（t-τ2）,…,u（t-τn））, t∈ R, where f：R×R^n＋1→R was a continuous function which wasω-periodic on t,and τ1,τ2,…,τn were positive constants.By establishing a new maximum principle,we constructed a monotone iterative procedure to seek theω-periodic solutions of the equation,and proved existence and uniqueness ofω-periodic solutions.