Growth And Angular Distribution Of Complex Differential Equations

In this thesis, we investigated some properties of solutions of the linear different-tial equations by using the value distribution theory and methods of Nevanlinna. The properties mainly contain the growth of solutions and the angular distribution. It includes following four chapters.Chapter1, We introduced the research background of linear differential equation-s. Then we narrate some notations and knowledge which will be used in the following chapters.Chapter2, By using the infinity order type function of Xiong Qinglai’s and a sufficient and necessary condition for infinity order Borel direction which was establi-shed by Chuang Chitai, we established the connection between the cluster ray of zero-sequence and Borel direction of solutions of second order differential equations f"+A(z)f=0, where A(z) is a meromorphic function of finite order.Chapter3, The growth of solutions of higher order linear differential equations with meromorphic coefficients is investigated by using the fundamental theory and method of Nevanlinna. Assume that one of coefficients has infinite deficient value, it is proved that every solution f≠0of the differential equation is of infinite order.Chapter4, The growth of solutions of higher order linear differential equations w-ith entire coefficients is investigated by using the fundamental theory and method of Nevanlinna. Assume that one of coefficients is extremal for Yang-Zhang inequality, it is proved that every solution f≠0of the differential equation is of infinite order.