Solutions Of Higher Order Complex Differential Equations

In this paper, we mainly use the research results and the existing methods and theory of complex differential equation, Wiman-Valiron and value distribution of meronorphic function theory and use the latest research methods and treatment for this kind of problems in the domestic and international to study the [, ] growth order of solutions of higher order complex differential equation(())+ -1()((-1))-1+ · · · + 1()(′)1+ 0() = 0where (), = 0, 1, · · ·, - 1 is analytic in the complex planeD.We also study the [, ] growth order of solutions of higher order linear equation()+ -1()(-1)+ · · · + 1()′+ 0() = 0where (), = 0, 1, · · ·, - 1 is entire function in the unit disc.There are three parts in this paper.In part 1(Introduction) We give an introduction of status and significance of research on this field in domestic and foreign, and bring in some related definitions and signs, and state the results that will be considered in this paper.In part 2(Chapter 2) We think over high order differential equation with their coefficient is analytic in the complex plane D. we research the [, ] order of the solution of differential equations.In part 3(Chapter 3) We rearch the the [, ] order growth of solutions of complex higher order differential equation in the unit disc.In part 4(Chapter 4) We summarized the research work, describe the deficiencies and what problems can we to continue to study in the future, analysis and prospect those problems.