非线性算子方程解的存在唯一性

Existence and Uniqueness of Nonlinear Operator Equation Solution

该文运用常微分初值问题(IVP)方法讨论了非线性算子方程F(x)=0解的结构。首先给出了IVP方法的一个改进结果,进而基于同伦变换思想得出了非线性算子方程解的存在唯一的条件。

The solution structure on nonlinear operator equation F（ x ） = 0 is studied by using Initial Value Prob- lem （IVP） method. Some results improved on IVP are presented. Based on the homotopy transform, the existence and uniqueness of the nonlinear operator equation solution is obtained.