The Order Of Growth And The Exponent Of Convergence Of The Solutions Of Some Classes Of Linear Differential Equations

Content In this thesis, we investigates the property of complex oscillation of some classes of higher order linear differential equations by applying with the theories and methods of the complex analysis. It includes the following four parts.In part 1 (Introduction), we give a brief introduction of the development history of this research field.In part 2(Chapter 1), we introduce some relevant definitions and some necessary notes, so that the readers can easily understand.In part 3(Chapter 2), we investigate the growth of meromor-phic solutions with infinite order of a class of higher order non-homogeneous linear differential equations with meromorphic coefficients. For most of meromorphic solutions, we obtain some precise estimates for their hyper order and their hyper exponent of convergence of the distinct zeros.In part 4(Chapter 3), we investigate the growth of solutions of a class of higher order homogeneous linear differential equation with meromorphic coefficients with iterated order. When the coefficient A0 is main dominating to the properties of the solutions, we obtain precise estimates of iterated order of the solutions.Part 3 and part 4 both improve the results obtained before.