一类三阶时滞微分方程在Banach空间中的周期解的存在性

Existence of periodic solutions of a class of third order delay differential equations in Banach spaces

利用上下解单调迭代方法,考虑有序Banach空间E中三阶时滞微分方程u″′(t)+M_0u(t-τ_0)=f(t,u(t),u(t-τ_1),u(t-τ_2)),t∈R,2π-周期解的存在性,其中f:R×E^3→E连续,关于t以2π-为周期,τ_0,τ_1,τ_2为正常数。通过建立新的极大值原理和构造方程2π-周期解的单调迭代求解程序,得到了该方程2π-周期解的存在性与唯一性结果。

Applying the monotone iterative method of upper and lower solutions,we discuss the existence of 2π-periodic solutions for the third-order differential equation with delays in ordered Banach space Eu″′（ t） ＋ M0u（ t-τ0）= f（ t,u（ t）,u（ t-τ1）,u（ t-τ2））, t∈R,where f：R × E3→E is a continuous function which is 2π-periodic in t,and τ0,τ1,τ2 are positive constants. By establishing a new maximum principle,a monotone iterative procedure for the equation is constructed. Some existence and uniqueness results of 2π-periodic solutions for this equation are obtained.