Reserches On The Value Distribution Theory And The Solutions Of Systems Of Higher-order Partial Differential Equations

In this paper,using the value distribution theory in several complex variables to investigate the problem of the existence of entire admissible solutions of two types of systems of higher-order partial differential equations on C~n.Using the Nevanlinna value distribution theory of meromorphic functions to investigate the value distribution ofφ(z)f~n(z)f′(z) in finite disc.There are three chapters.In the first chapter,we simply introduce the elementary knowledge of the value distribution theory in several variables and fundamental theorems in Nevanlinna value distributions theory,some usual notations,definitions and fundamental theories.In the second chapter,we consider the existence of integer admissible solutions of two types of systems of partial differential equations on C~n;And some Malmquist type theorem in C~n which is similar as that of differential equations in C are established;Some important result of partial differential equation in C~n are extended to the systems of partial differential equations on C~n.In the third chapter,we discuss the value distribution of meromorphic functions of the differential monomialφ(z)f~n(z)f′(z),obtain a better result and generalize some known conclusions obtained by Zhang Qingde etc..