Applications Of Nevanlinna Theory In The Systems Of Complex Differential Equations

This thesis mainly investigates the application of Nevanlinna theory in systems of higher-order complex differential equations. Except the introduction, We discuss them in five sections.Firstly, we mainly introduce the basic definitions and fundamental theorems of Nevanlinna'svalue distribution theory.Secondly, conceming the growth ofmeromorphic admissible solutions,we study meromorp-hie solutions of systems of complex differential equations, figure out the estimation on solutionsof some special systems of differential equations and get a main result.Thirdly, referring to the form of complex differential equations:on the one hand, we introdu-ce some results relevant to this field and further discuss the change of complex differentialequation as meromorphic solutions exist;on the other hand, we give a further discussion on someresults in relation to this field, improve a main result and deeply do some research on thecharacteristic estimation.Next, regarding the existence of non-admissible solutions, through studying problems onthe growth of meromorphic solutions of systems of higher-order complex differential equationsin certain circumstances, we chiefly figure out the existence of non-admissible solutions of aspecial type of higher-order complex differential equations and testify a main result.Finally, we conclude series of results,give some own ideas and guesses about someinteresting unresolved problems,which are in favor of doing some further research in the future.