α-Normal Functions and Complex Differential Equations

ΜOS subject classification Categories: 30D50, 34A20

Abstract A function f meromorphic in the unit disk D is called an α-normal if sup _z∈D ∈(l - |z|²)α f ^#(z) < ∞, α > 0, where f ^#(z) = 3D|f′(z)|²). Some integral characterizations and the value distribution of α-normal functions are given. The relationship between α-normal functions and the meromorphic solutions of algebraic differential equations are also considered.