Growth and oscillation of differential polynomials in the unit disc.

Abstract

In this article, we give sufficiently conditions for the solutions and the differential polynomials generated by second-order differential equations to have the same properties of growth and oscillation. Also answer to the question posed by Cao [6] for the second-order linear differential equations in the unit disc. 1. Introduction and main results The study on value distribution of differential polynomials generated by solutions of a given complex differential equation in the case of complex plane seems to have been started by Bank [1]. Since then a number of authors have been working on the subject. Many authors have investigated the growth and oscillation of the solutions of complex linear differential equations in C, see [2, 4, 7, 1 0, 1 3, 1 7, 1 8, 1 9, 2 1, 25, 28]. In the unit disc, there already exist many results [3, 5, 6, 8, 9, 1 5, 1 6, 20, 23, 24, 29], but the study is more difficult than that in the complex plane. Recently, Fenton-