Studies On Uniqueness Of Meromorphic Functions With Their Differences In Several Complex Variables And Complex Partial Differential Difference Equations

Nevanlinna theory is an important tool for studying the uniqueness of meromorphic functions and the value distribution problem of complex differential equations.In this thesis,making use of difference analogues of Nevanlinna theory for meromorphic functions in several complex variables,we study the uniqueness problem for meromorphic functions with their differences in several complex variables,the difference Clunie type theorem in several complex variables,the existence of admissible solutions of a class of systems of partial differential-difference equations and the property of solutions of linear nonhomogeneous partial q-difference equation.The thesis is structured as follows:In chapter 1,we introduce the research background and main research content of this thesis.In chapter 2,we introduce some basic concepts of Nevanlinna theory of several complex variables.In chapter 3,we obtain the second main theorem for meromorphic functions with the n-th exact difference and the second main theorem for meromorphic mappings with Casorati determinant on(?)~m.By using the conclusion,we generalize some results of the uniqueness for meromorphic functions of one complex variable and their differences sharing values or small functions to several complex variables.In chapter 4,drawing on the method in Korhonen's article,we use difference version of logarithmic derivative lemma on(?)~m extend the difference Clunie type theorem in one complex variable to several complex variables.In chapter 5,we study the existence of admissible solutions of a class of systems of partial differential-difference equations and the growth of solutions of linear partial q-difference equation of the nonhomogeneous form on(?)~m.In chapter 6,we give the summary of this thesis and direction of further work.