混合型单调算子对的不动点及其应用

Fixed Point of Mixed Type Monotone Operator and Its Application

提出了混合型单调算子对的概念,利用混合型单调算子对的定义及数学归纳法对混合型单调算子对的不动点的存在性及唯一性进行了证明,得出了混合型单调算子对的不动点若存在必唯一的结论。该结论应用于带奇性的一阶非线性常微分方程组的初值问题。

In this paper, we give the definition of the mixed type monotone operator,then we prove the existence and the unique of the fixed point of the operator with induction.Furthermore we prove the fixed point is unique if it exists.Finally we give the application in differential equation group.