The Borel Direction Of Meromorphic Function With Iterated Order And The Complex Oscillation Theorey Of Solutions Of Differential Equations

In this thesis, we investigate the Borel direction of the meromorphic functions with iterated order and the complex oscillation theory of solutions of differential equations by using the concept of iterated order. It includes following four chapters.In chapter 1, we introduce the definitions concerning iterated order of meromorphic function. In chapter 2, we investigate the Borel exceptional values, full circles, and Borel directions of iterated order of meromorphic functions .In this thesis, we investigate the property of solutions of differential equations with coefficients of iterated order. In chapter 3. we investigate growth problems of solutions of one type of homogeneous and non-homogeneous higher order linear differential equations with entire coefficients of iterated order. For this type of equations, we obtain precise estimate of iterated order and iterated covergence exponent of the zeros of solutions when some coefficient or free term is main dominating to the properties of the solutions. In chapter 4 , we investigate complex homogenous and non-homogeneous higher order linear differential equations with meromorphic coefficients of iterated order. We obtain several results concerning the iterated order of meromorphic solutions, and the iterated convergence exponent of the zeros of meromorphic solutions. We also improve the results obtained by some authors.