Banach空间中的常微分方程边值问题的拟上下解方法

Method of Quasi-Upper and Lower Solutions to Boundary Value Problem of Ordinary Differential Equations in Banach Space

摘要:

利用拟上下解方法,研究了一阶非线性微分方程边值问题 u′(t) =f (t,u(t)),u(0) -u(T) =x1,x1 ≥0拟解的存在性,并通过线性微分方程的解来构造算子,从而得到单调迭代序列,进而得到该边值问题的最大最小拟解对。

Abstract:

The existence of quasi solution for the boundary value problem of one-order nonlinear ordinary differential equa.f () , u()u() tion u ′()t =t,u()t 0-T =x1,x1≥0 was studied by making use of the quasi upper-lower solution method. Andthe operator was constructed by the solution of the linear differential equation. Furthermore, the monotone iteration se.quences were gotten, and finally the maximum-minimum quasi-solution pair was obtained.