Researches On The Value Distribution Theory And Solutions Of Systems Of Non-linear Higher-order Differential Equations

Using the Nevanlinna value distribution theory of meromorphic function, we investigate the solutions of systems of non-linear higher-order differential equations and the value distribution of differential monomials. Some theorems, which are improvements and generalizations of some known results on the topic, are obtained.The thesis is divided into four sections.The first chapter briefly introduces the element knowledge of Nevanlinna value distribution theory, including usual notations, definitions and fundamental theorem and Malmquist theory.The second chapter investigates the non-admissible components of solutions of systems of non-linear higher-order differential equations. Given the condition, we obtain that the n-components of solutions of non-linear higher-order differential equations are non-admissible.In chapter three and chapter four, we study the value distribution of differential monomials. Some new results on the topic are obtained.