Researches On The Solutions Of One Type Of Systems Of Higher-order Complex Differential Equations

The problem of systems of complex differential equations is a fringe field which rose from the late 1980s, its study requires multi-subject. The main tools of the study are the theory of Nevanlinna value distribution, Wiman-Valiron theory etc. Many scholars introduced the notion of admissible solution on their study on the systems of some algebraic differential equations, but there were so many literatures have done more thorough research on admissible solutions. In this paper, we will discuss the non-admissible solution questions of the systems of equations.By means of the Nevanlinna value distribution theory of meromorphic functions, we investigate the existence of non-admissible solutions and the counting fuctions of meromorphic solutions of a type of systems of higher-order algebraic differential equations(?),get several theorems which are improvements and generalizations of some known results on this topic.This article include three chapters. The first chapter simply introduce the elementary knowledge of Nevanlinna value distribution theory, including the Poisson-Jensen formula, the notion of characteristic function and its character, the first fundamental theorem and the second fundamental theorem, as well as logarithmic derivative lemma and its deductions; Second chapter have introduced the notions of admissible solution and non- admissible solution, using the method of disproval, have given non- admissible solution existence conditions of the above system of equations; Third chapter further discuss the counting functions of meromorphic solutions of the system of equations, discovering that under the certain condition, the number of poles of admissible solutions component of order at leastM nearly is zero,and each pole according to its multiplicity respectively, that is said, N₍(M)(r,w_i)is the small functionS(r,w).