Some results on the regular solutions of a linear differential equation
In this paper, we prove a theorem on the regular growth of the solutions of a linear differential equation, as an application of which we obtain some uniqueness theorems of an entire function sharing a finite nonzero complex number with its nth derivative and a linear differential polynomial of its nth derivative under the restriction of finite lower order or of finite lower hyper-order that is not a positive integer. The results in this paper improve many known results. Some examples are provided to show that the results in this paper are the best possible. (C) 2008 Elsevier Ltd. All rights reserved.
uniqueness theorems entire functions shared values order of growth