The Properties Of Solutions Of Some Types Of Linear Differential Equations In The Complex Plane And The Unit Disc

In this thesis, we investigate the complex oscillation properties of the solutions of some typesof linear diferential equations by applying the theories and methods of the complex analysis. Itcontains the following five parts.Part1: we give a brief research with present situation in home and abroad.Part2: we introduce some preliminary knowledge, which contains mainly some definitionsand marks we need.Part3: we investigate the relation between solutions of a class of second order of lineardiferential equation with entire coefcients with function of small growth. We obtain the relationbetween the solutions, their1th,2th derivatives, diferential polynomial of the equation withfunction of small growth.Part4: we investigate the property of complex oscillation of a class of higher order nonho-mogeneous linear diferential equation with meromorphic coefcients. We obtain the property ofexponent of convergence and order of the solutions of the equation and improve the results of theequation with entire coefcients to the equations with meromorphic coefcients.Part5: we investigate the property of the solutions of some types of higher-order lineardiferential equations in the unit disc. We obtain the property of exponent of convergence andorder of the solutions of the equation and obtain in which space the solutions of the equation. Weimprove the result obtained before.