一类半线性算子方程解的存在唯一性

Existence and Uniqueness of Solution for One Kind of Semi-Nonlinear Operator Equation

使用常微分方程初值问题(IVP)方法讨论了半线性算子方程Lu+N[u]=F(u)是否有解.首先基于同伦变换思想得到了方程Lu+N[u]=f解存在的充分必要条件、解唯一的必要条件和解的一个估计,进一步得到了方程Lu+N[u]=F(u)有解的条件.

The existence of solution for semi-nonlinear operator equation is studied by using Initial Value Problem （IVP） method. First, the equation is discussed by homotopy deformation, and a necessary and sufficient condition for the existence of the solution, a necessary condition for the uniqueness of the solution and an estimation of the solution are obtained. Furthermore, the equation is discussed by using similar method, and the conditions for the existence of the solution of the equation are presented.