Some results on the regular solutions of a linear differential equation

✍ Scribed by Xiao-Min Li; Hong-Xun Yi

• Publisher: Elsevier Science
• Year: 2008
• Tongue: English
• Weight: 371 KB
• Volume: 56
• Category: Article
• ISSN: 0898-1221
• DOI: 10.1016/j.camwa.2008.03.046

✦ Synopsis

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.