The Order Of Solutions Of Complex Differential Equations In Angular Domains And Singular Directions

In this thesis,we investigate some analytical properties of second order linear differential equations in angular domains by using Nevanlinna's value distribution theory.The thesis includes the following five parts.In the first part,the research significance,background,and the development of the thesis are introduced,and the basic definitions,theorems and symbols are also given in this part.Moreover,we introduce the Nevanlinna value distribution theory in an angular domain and some results of Wiman-Valiron theory.In the second part,by using the infinity order type function of Xiong Qinglai's and a sufficient and necessary condition for infinity order Borel direction which was established by Chuang Chitai,we discuss the relationship between Borel directions of precise order of solutions of second order nonhomogeneous linear differential equation and that of nonhomogeneous term,and also obtained the connection between zero accumulation ray of precise order of solutions and that of the derivative of the solution on second order linear differential equation.In the third part,we study the order and Borel directions of solutions of differential equations.With some added conditions on coefficients,we can guarantee that every solution of the equation has infinite order and has at least two Borel directions in a certain angular domain.In the fourth part,we consider the Borel directions of solutions of the differential equation.If one coefficient is extremal for Yang's inequality,and posing some conditions on the other coefficient,we can guarantee that every non-trivial solution of the equation is of infinite order and obtain the number of the Borel directions of solutions.In the fifth part,we generlize the results of the thesis and give some expectations.