Researches On The Growth Order Of Solutions Of Systems Of Differential Equations And Related Problems

In this thesis, the higher order of two types of systems of complex algebraic differential equationsare investigated about the growth of their solutions by the theory of Nevanlinna's value distribution of meromorphic function and the theory of normal family. Meanwhile, we discuss the value distribution about the product of functions and its derivatives and related results.Four chapters are composed of this thesis. Chapter 1 introduces the elementary knowledge of the theory of Nevanlinna's Value distribution, including Poisson-Jensen formula, the character functions of meromorphic function and related concepts and results. Chapter 2 includes the notion of the normal family of meromorphic function, Zalcman's lemma and Bergweiler's lemma, and researches the growth of solutions of the higher order of two types of systems of complex algebraic differential equations, and derives more satisfying results that the growth of solutions of the systems (1)and (2) are finite. Chapter 3 mainly investigates the value distributionof the product of functions and its derivatives f^kfⁿ and gains some new results. Moreover,these results contain the related results. We obtain the Milloux inequality about the homogeneous differential polynomial in chapter 4.