Some Kinds Of Bounded Variation Solutions Of Nonlinear Integral Equations In Multidimensional Space

In this paper,we study the existence and uniqueness of several kinds of bounded variation solutions for two kinds of nonlinear integral equations(nonlinear Hammerstein integral equation and nonlinear Volterra-Hammerstein integral equation).In this paper,we construct a new bounded variation space and give the existence condition of new bounded variation solution.In the first chapter,we first review the practical significance of the research on the theory of bounded variation,and then derive the concept of bounded variation.We review the research process of the definition of bounded variation and related properties,and the extension process of the definition of bounded variation from one-dimensional space to multidimensional dimensional space.We review the definition of two kinds of nonlinear integral equations.Introduce the concept of bounded variation solution of nonlinear integral equation,and then describe the research status and significance of this kind of problem.In chapter two,the existence conditions of(?1,?2)bounded variation solutions for two kinds of nonlinear integral equations are studied.The research process of nonlinear integral equation and bounded variation solution is reviewed.The basic form of integral equation defined in two-dimensional space is introduced.The normed space of(?1,?2)bounded variation is constructed and the norm definition is given.It is proposed that,in this space,the existence of a unique,(?1,?2)bounded variation solution of the integral equation can be obtained by limiting the parameters of the integral equation under some conditions.Then proof.In chapter three,the existence conditions of ?n bounded variation solutions for two kinds of nonlinear integral equations are studied.The normed space of bounded variation is constructed and the space norm is defined.The definition forms of two kinds of nonlinear integral equations in n dimensional space are introduced.Some restrictions are given for the parameters of the new integral equation so that there exists a unique,?n bounded variation solution in this space,and the proof is given.