The Complex Oscillation On Solutions Of Several Kinds Of Higher Order Linear Differential Equations

In this thesis, we investigate the complex oscillation properties of solutions of some types of higher order linear differential equations by applying the theories and methods of the complex analysis. It consists of the following three chapters.In chapter1, we give a brief introduction of the development history of this research field and lead into some related definitions, theorems and necessary signs.In chapter2, we investigate the order and the hyper-order of solutions of the higher order linear differential equations and Under some conditions, we prove that every solution f(≠0) of the equations is of infinite order and σ2(f)=1. And we also investigate the complex oscillation proper-ties of solutions of the higher order linear differential equation Under some conditions, we obtain some precise estimations of the order, the exponent of convergence of zeros and so on.In chapter3, considering the case that the equation in Th2.3may have one exceptional solution with finite order, we continue to investigate the order of solutions of the higher order linear differential equation Under some conditions, we prove that every solution of the above equation is of infi-nite order.