Acta mathematica scientia,Series A ›› 2021, Vol. 41 ›› Issue (1): 69-80.

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The Non-Existence of Solutions of a Certain type of Nonlinear Complex Differential-Difference Equations

Shuqing Lin(),Junfan Chen*()   

  1. College of Mathematics and Informatics & Fujian Key Laboratory of Mathematical Analysis and Applications, Fujian Normal University, Fuzhou 350117
  • Received:2020-02-14 Online:2021-02-26 Published:2021-01-29
  • Contact: Junfan Chen E-mail:shuqinglin1996@163.com;junfanchen@163.com
  • Supported by:
    Supported by the NSFC(11301076);the NSF of Fujian Province(2018J01658);the NSF of Fujian Province(2019J01672)

Abstract:

In this paper, we study transcendental entire solutions of a certain type of complex differential-difference equations where $P(z) $ and $Q(z) $ are non-zero polynomials, $\alpha(z) $ is polynomial, $ m$ and $n $ are positive integers, $ \eta\in{\Bbb C}\setminus\{0\}$. Several sufficient conditions on the non-existence of transcendental entire solutions of such equations are supplied.

Key words: Complex differential difference equation, Transcendental entire solution, Nevanlinna theory, Finite order

CLC Number: 

  • O174.52
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