On The Growth Of Solutions Of The Second Order Linear Complex Differential Equation

In this thesis, we investigate the complex oscillation properties of the solutions ofsome types of linear differential equations by applying the theories and methods of thecomplex analysis. It includes following four chapters.Chapter1: We give a belief introduction of the development history of thisresearch and introduce the preliminary knowledge.Chapter2: In this chapter，by using the fundamental theory and method ofNevanlinna， the growth of solutions of the second order linear differentialequations f"+Af’+Bf=0is considered where A(z)and B(z)are meromorphicfunction. Assume A(z)or B(z)has a finite or infinite deficient value, it wasproved that every solution f≠0of the complex differential equation has infiniteorder.Chapter3: In this chapter，we investigate the growth of meromorphic solutionswith infinite order of a class of second order linear differential equations withmeromorphic coefficients. Under some conditions, it is proved that every solutionf≠0of the equation is of infinite order, and estimate it’s super order.Chapter4: In this chapter，the growth and Borel directions of solutions in angulardomains of differential equation f"+Af’+Bf=0is investigated where A(z)andB(z)are entire functions, by using the fundamental theory and method of valuedistribution in angular domain. Under some conditions, it is proved that every solutionf≠0of the equation is of infinite order in any angular domain which has orderBorel direction of B(z), and the infinite order Borel direction of the solution isunanimous with the order Borel direction of B(z).