The Complex Oscillation Properties Of The Solutions Of Some Types Of Linear Differential Equations

Content:In this thesis,we investigate the complex oscillation properties of the solutions of some types of linear differential equations by applying the theories and methods of the complex analysis.lt contains the following five parts:In part 1, we give a brief introduction of history on development of this research field.In part 2,we introduce some preliminary knowledge,which is mainly definitions and marks of some concepts used in later chapters.In part 3, we investigate the property of complex oscillation of the solutions of a type of higher-order linear differential equation with entire coefficients. We obtain some precise estimates of the growth of the solutions of the equation and improve the result obtained before.In part 4,we investigate the property of complex oscillation of the solutions of some types of higher-order linear differential equations with meromorphic coefficients.We obtain some precise estimates of the growth of the meromorphic solutions of the equations,and improve the results of the equations with entire coefficients to the equations with meromorphic coefficients.In part 5,we investigate the problems on the fixed points and hyper order of solutions and their 1^st,2^nd derivatives of a class of second order linear differential equations with meromorphic coefficients. We obtain the precise properties of fixed points of meromorphic solutions of complex differential equations.