On The Oscillation Of Meromorphic Solutions Of Linear Differential Equations

In this paper,we mainly study the complex oscillation of solutions of differential equations on meromorphic function coefficients,and respectively consider two kinds of equations,including the second order and the higher order.It includes the following four parts.In part 1(Introduction),we give an introduction of present situation of this field in domestic and foreign,bright in some related definitions and signs,and give the questions that in this paper will be considered.In part 2(Chapter 2),we study the result made by Kwon Ki-Ho of the second order differential equations on entire function coefficients.In some conditions,we obtain the similar parts of conclusions of the second order differential equations on meromorphic function coefficients.In part 3(Chapter 3),we investigate the growth of solutions of the second order differential equations on entire function coefficients.We obtain the similar conclusion of higher order differential equations on meromorphic function coefficients,when some coefficients of equations satisfy some special conditions.In part 4(Chapter 4),we study the growth of solutions of one kind of higher order differential equations on meromorphic function coefficients.To some extent,we improve the result made by Chen ZongXuan and Xiao LiPeng,and we obtain the precise estimations of meromorphic solutions of the equations on higher order linear differential equations.