一类三阶时滞微分方程在Banach空间中的周期解的存在性

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)+M₀u(t-τ₀)=f(t,u(t), u(t-τ₁), u(t-τ₂)),〓t∈R,2π-周期解的存在性, 其中 f: R×E³→E 连续, 关于 t 以 2π-为周期, τ₀,τ₁,τ₂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。

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

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.