The Complex Oscillation On Meromorphic Solutions Of Several Types Of Higher Order Liner Differential Equations

In this thesis, by using the Nevanlinna’s value distribution theory and the Wiman-Valiron theory, we mainly investigate the complex oscillation properties of solutions of several types of linear differential equations. It includes the following four chapters.In chapter 1, we give a brief introduction of the development history of the complex oscillation of differential equations and the research background of this article. We also give some relevant definitions and notations used in this thesis.In chapter 2, we investigate the growth of meromorphic solutions of differen-tial equations and where Aj(j= 0,1, …, k- 1), F are meromorphic functions. When there exists one dominant coefficient with lower order less than 1/2, we obtain some estimations of the hyper order and the hyper convergence exponent of zeros of meromorphic solutions of the above equations.In chapter 3, we investigate the growth of solutions of higher order linear differential equation where Ak-1,…, A0((?) 0) are meromorphic functions. Suppose that most coef-ficients in such equation have the same order, we give some conditions which guarantee that each solution f((?)0) of such equation has infinite order. We also obtain the precise estimation of growth of infinite order solutions. And the properties of the fixed points of solutions are also considered in this chapter.In chapter 4, the growth of solutions of the higher order homogeneous linear differential equation and its non-homogeneous differential equation are investigatived, where Aj(z)(j= 0,1,…, k-1) are meromorphic functions with at most finitely many poles and its order is less than n, Pj(z) are nonconstant polynomials. Under certain conditions, some estimations of the order of solutions for such equations are obtained.