二阶多时滞微分方程周期解的存在性

摘要

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-τ1),u(t-τ2),…,u(t-τn)), t∈Rω周期解的存在性,其中:f:R×Rn+1→R连续,关于t以ω为周期;τ1,τ2,…,τn为正常数.通过建立新的极大值原理,构造方程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 of ω-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 × Rn+1→R was a continuous function which was ω-periodic on t,and τ1,τ2,…,τn were positive constants.By establishing a new maximum principle,we constructed a monotone iterative procedure to seek the ω-periodic solutions of the equation,and proved existence and uniqueness of ω-periodic solutions.