The Existence Of Solutions For Two Kinds Of Nonlinear Operators

In this thesis,we study the fixed point theorem of the set-valued mixed monotone operator and the existence of solutions for the nonlinear integro-differential equation of mixed type.This paper is divided into three chapters:In the first chapter,we introduce the background of the problem and the main results of this thesis.In the second chapter,we investigate the coupled fixed point of the set-valued mixed monotone operator with the form of A-CB and the existence of its minimal maximal coupled fixed point in the semi-ordered topological space.In the third chapter,we discuss the existence of solutions for the nonlinear integro-differential equation of mixed type in a Banach space:(?).