Growth estimates for meromorphic solutions of higher order algebraic differential equations

Abstract

We establish pointwise growth estimates for the spherical derivative of solutions of the first order algebraic differential equations. A generalization of this result to higher order equations is also given. We discuss the related question of when for a given class X of meromorphic functions in the unit disc, defined by means of the spherical derivative, and m ∈ N \ {1}, f m ∈ X implies f ∈ X. An affirmative answer to this is given for example in the case of UBC, the α-normal functions with α ≥ 1 and certain (sufficiently large) Dirichlet type classes.