In this thesis,we investigate the growth of solutions of complex linear differential equations and functional spatial properties of solutions to several types of nonlinear complex differential equations,some conditions which guarantee every nontrivial solution of the complex linear differential equations to belong to infinite order and guarantee analytic solutions of the nonlinear complex differential equations to belong to some functional spaces are obtained in this paper,which generalize existing results.This thesis include three chapters.The relevant knowledge of Nevanlinna theory is recalled and the progress of solutions of complex differential equations is introduced in the chapter 1.The growth of solutions of higher order complex linear differential equations is studied in the chapter 2.Functional spatial properties of solutions to several types of nonlinear complex differential equations is studied in the chapter 3. |