Research On Some Problems About Solution Of Nonlinear Operator Equation

Operator equation and the fixed point problem are an important component of nonlinear functional analysis theory.They are playing important role in solving nature and uniqueness problems about all kinds of differential equations and integral equations.Consequently,the research of nonlinear operator equation and the fixed point is of great significance.In this thesis,some problems about the solution of nonlinear operator equations in probabilistic metric space and partial order bananch space are studied.It is divided into the following four sections.In chapter one,the backgrounds and current situation about the solution of nonlinear operator equations in probabilistic metric spaces are introduced and the preliminaries are given.In chapter two,we will use the method of topology degree mainly to study two operator equations about(Tx=μx(μ≥1) and Tx=x)in probability metric space and Z-P-S space,and get a few new conclusions.In chapter three,we will use the method of topology degree mainly to study the existence of intrinsic value and intrinsic element in the Z-P-S space,and get some new results.In chapter four,we will use the method of iteration to study the existence of solution of monotone operator equation in partial order Banach space,and get a few new theorems.