一阶混合单调脉冲微分方程解的存在性

Existence of Solutions for the First Order Mixed Monotone Type of Pulse Differential Equations

脉冲微分方程理论是微分方程的一个重要分支,混合单调迭代技术是其重要基础之一。在Banach空间中,利用混合单调迭代技术及Shaulder不动点定理,考虑混合单调脉冲微分方程初值问题,给出方程解和藕合最大最小解的存在性定理及单调迭代方法。

The theory of pulse differential equation is an important branch of differential equations. The monotone iterative technique is one of its major bases. Within Banach space, by using the mixed monotone iterative technique and Shaulder fixed point theorem, taking into consideration the initial value of the mixed monotone type of pulse differential equations, I draw the solution of equation, the theorem that its coupled minimal and maximal quasisolutions exist. I also give the monotone iterative method.