Solution of a differential equation and its applications

Abstract

In this paper, we proved that the order of entire solutions of the differential equation /^ -fe®^ = 1 are infinite, where Q(z) is a nonconstant polynomial, and gave some of its applications.

Growth of solutions of a class of complex differential equations

“…The idea is taken from [6], [7] or [9], and it is very different from Yang [22]. Now we show our main result which improves Theorem 1.1 and some results in [18], [20], [9]. Theorem 1.2.…”

A Further Result Related to a Conjecture of R. Brück

“…In 1999, Yang [10] confirmed that the Conjecture is also true when f is replaced by f (k) (k ≥ 2) and f is of finite order. In recent years, many results have been published concerning the above conjecture, see [2,5,7,8,14,15,16,17,18] etc., and Zhang [17] was the first author who considers the case when f is a meromorphic function.…”

Non-existence of meromorphic solutions of a Fermat type functional equation

“…In 1998, G. G. Gundersen and L. Z. Yang proved in [6] that the conjecture is true if f is of finite order. In 1999, L. Z. Yang proved in [7] that the same result holds if f ′ is replaced by f (k) (k ≥ 2). Up to now, R. Brück's conjecture is still open.…”