Study On The Value Distribution Properties Of Solutions Of A Class Of Second-order Differential Equation

The thesis uses the theory of value distribution on meromorphic function to study the growth and dynamics properties of non-trivial solutions of a class of second-order complex differential equations.The thesis is divided into three chapters.The main content of each chapter is as follows:In the first chapter,we briefly review the development of the value distribution theory and the historical background of the research content of this thesis.Then,we describe in more detail the definitions and notations needed,which help us to explain our main results and proof.In the second chapter,we studied the growth of complex linear differential equation f"+A(z)f'+B(z)f=0,where the coefficient functions A(z)and B(z)are both entire functions.We proved that the growth order of the non-trivial solution of the equation under several coefficient conditions is infinite,and obtained a positive lower bound estimation for the linear measure of the angular set where the radial growth order is infinite.In the third chapter,we continued to study the problem of the limit direction of the non-trivial solution of this complex differential equation with different coefficients from that of the second chapter.With the given coefficients,we proved that the order or the lower order of the non-trivial solution of the equation is infinite,and obtained a positive lower bound estimation for the linear measure of the set,which is formed by common limit directions of Julia set.