Growth Of Meromorphic Solutions Of Some Types Of Homogeneous And Non-homogeneous Linear Differential Equations

In this thesis, we make use of Nevanlinna value distribution theory and thebasic knowledge of complex linear diferential equations. When the coefcientsare meromorphic functions in complex plane or analytic functions in the unitdisc respectively, we investigate some properties of solutions of linear diferentialequations. This thesis is divided into four chapters.In chapter1, we simply introduce the development of the theory of complexoscillation, as well as the definitions and some basic notations about meromorphicfunctions and analytic functions in complex plane and in the unit disc respectively.In chapter2, we investigate growth of solutions of some higher order ho-mogeneous and non-homogeneous linear diferential equations with meromorphiccoefcients, and obtain some results on the iterated order of the solutions undercertain conditions. Moreover, we also give some estimations on the iterated ex-ponent of convergence of zeros and the points where the solutions take the samevalue with small functions.In chapter3, we investigate growth of solutions of higher order homogeneouslinear diferential equations with special meromorphic coefcients. Under thecondition that meromorphic coefcients have the same order, we obtain preciseestimations on the hyper order of the solutions of infinite order. Moreover, wealso investigate the hyper order and the hyper exponent of convergence of zerosof meromorphic solutions of the corresponding non-homogenous linear diferentialequations.In chapter4, we investigate growth of solutions of second order and higherorder linear diferential equations in the unit disc. When the coefcients areanalytic functions, we obtain precise estimations on the order and hyper order ofsolutions of the equations.