Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2013; 50(5): 1471-1479

Printed September 1, 2013

https://doi.org/10.4134/BKMS.2013.50.5.1471

Copyright © The Korean Mathematical Society.

On entire solutions of nonlinear difference-differential equations

Songmin Wang and Sheng Li

The Chinese People's Armed Police Forces Academy, Guangdong Ocean University

Abstract

In this paper, we study the non-existence of finite order entire solutions of nonlinear differential-difference of the form $$f^n+Q(z,f)=h,$$ where $n\ge 2$ is an integer, $Q(z,f)$ is a differential-difference polynomial in $f$ with polynomial coefficients, and $h$ is a meromorphic function of order $\le1$.

Keywords: difference-differential polynomial, differential polynomial, differ\-ence-differential equation, Nevanlinna theory

MSC numbers: 39B32, 34M05, 30D35