The Complex Oscillation Theory Of Solutions Of Some Differential Equations With Entire Coefficients

Content : In this thesis, we investigate the problem on the properties of complex oscillation of solutions of some linear differential equations with entire coefficients.In chapter 2, we study the orders of growth and the exponents of convergence of the zero-sequence of solutions of a class of higher order linear differential equations, in these equations, there are some coefficients with the same order of growth, among which if two coefficients such as As and Al satisfy σ(As/Al) < σ(As), we get some results of the proper es of solutions of the class of homogeneous and non-homogeneous linear differential equations.In chapter 3, we investigate the growth of solutions of certain second order linear differential equations f" + A(z)f' + B(z)f = 0. Under the condition of σ(B) < σ(A), in order to get the result that the order of every solution f((?) 0) is infinite, one often gives the additional limitation that the order of one of the two coefficients is smaller than 1/2. In this chapter , under the condition of σ (A) > σ(B) > 1, we investigate this type of differential equation and estimate the hyper-order of solutions of infinite order.