Value distribution for solutions of complex differential equations in the unit disk

In this dissertation we consider complex differential equations where the coefficients are meromorphic functions in the unit disk. We estimate the growth and the value distribution of the solutions with regard to the growth and value distribution of the coefficients of the equation. Particularly we determine solutions of slow growth as measured by the Nevanlinna characteristic function.; We first consider algebraic differential equations using an approach by Zalcman for normal families to extend some results obtained in the plane and in the unit disk when the coefficients are analytic to the case where the coefficients are meromorphic.; We then consider homogeneous linear differential equations of order n with analytic coefficients of slow growth applying techniques of order reduction as used by Frei and Wittich for the planar case.; The same linear differential equation is considered in the investigation of the growth of the number of zeros of a product of n + 1 analytic solutions, any n of which are linearly independent. Here a Cartan approach to a fundamental system for a differential equation is used extensively.; Second order differential equations with coefficients of slow growth are also examined with more emphasis on value distribution and Borel exceptional values. The more general linear differential equations, homogeneous and non-homogeneous, are then studied with a similar perspective. Aspects of Nevanlinna theory form the basis for the proofs in this section.; Finally, we obtain results for non-linear differential equations of the Riccati type.