The Properties Of Solutions Of Several Linear Differential Equations With Transcendental Entire Function Coefficients

In this thesis,we make use of Nevanlinna value distribution theory, Wiman-Valiron theory, potention theory and the basic knowledge of complex linear differential equations. To investigate some properties of solutions of linear differential equations, we assume the coefficients of linear differential equations are transcendental entire functions in complex plane. This thesis is divided into four parts.In the first part, we introduce the research status of this research field both at home and abroad and the definitions and some some basic notations about meromorphic functions and analytic functions in complex plane.In the second part, we investigate growth of solutions of higher order homogeneous linear differential equations with transcendental entire functions coefficients.Under the condition that transcendental entire functions coefficients have the same order, we obtain precise estimations on the hyper order of the solutions of infinite order. Moreover, we also investigate the hyper order and exponent of convergence of zeros of solutions of the corresponding non-homogenous linear differential equations.In the third part, we investigate the relation between solutions of a class of second order homogeneous linear differential equation with transcendental entire functions coefficients with function of small growth. We obtain the relation between the solutions, their 1th, 2th derivatives,differential polynomial of the equation with function of small growth.In the fourth part, we investigate the existence and the representations of all subnormal solutions of a class of second order homogeneous linear differential equation with periodic coefficients.