Growth And Value Distribution Of The Solutions Of Homogeneous Linear Differential Equations In The Complex Plane And The Unit Disc

In this thesis, we mainly make use of Nevanlinna theory to investigate the growthand the value distribution of the solutions of higher order homogeneous linear diferentialequations with meromorphic coefcients being transcendental. This thesis is made up offour chapters.In chapter1, we briefly introduce the development in the field of complex lineardiferential equations. And some basic definitions and normal notations in the complexplane and in the unit disc have also been given.In chapter2, we investigate the growth of the solutions of higher order homogeneouslinear diferential equations with meromorphic coefcients of finite iterated orders in thecomplex plane. We also investigate the value distribution of these points, where thederivatives of arbitrary order of the solutions share the same value with small function(z), and precise estimates on the iterated (lower) convergence exponent of these pointshave also been given.In chapter3, we investigate the growth and value distribution of the solutions ofhigher order homogeneous linear diferential equations with meromorphic coefcients of[p, q]-orders in the complex plane, after having investigated the case that meromorphiccoefcients have finite iterated orders in chapter2. And some similar results are obtained.In chapter4, we continue to investigate the solutions of higher order homogeneouslinear diferential equations with analytic coefcients of [p, q]-orders in the unit disc andsome results on the growth and value distribution of the solutions are given under someconditions.