The general result of Gol’dberg’s theorem concerning the growth of meromorphic solutions of algebraic differential equations

Abstract

In this paper, we give a general estimate result of Gol’dberg’s theorem concerning finite growth order of meromorphic solutions of first-order algebraic differential equations by using the normal family theory. It is an extending result of corresponding theorem for Bergweiler and Barsegian and so on. We also give some examples to show that our result is sharp in special case.