Bulletin of the
Korean Mathematical Society
BKMS

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

Article

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Bull. Korean Math. Soc. 2023; 60(2): 425-441

Online first article March 21, 2023      Printed March 31, 2023

https://doi.org/10.4134/BKMS.b220170

Copyright © The Korean Mathematical Society.

On meromorphic solutions of nonlinear partial differential-difference equations of first order in several complex variables

Qibin Cheng, Yezhou Li, Zhixue Liu

Beijing University of Posts and Telecommunications; Beijing University of Posts and Telecommunications; Beijing University of Posts and Telecommunications

Abstract

This paper is concerned with the value distribution for meromorphic solutions $f$ of a class of nonlinear partial differential-difference equation of first order with small coefficients. We show that such solutions $f$ are uniquely determined by the poles of $f$ and the zeros of $f-c, f-d$ (counting multiplicities) for two distinct small functions $c, d$.

Keywords: Several complex variables, meromorphic solutions, partial differential-difference equation, value distribution

MSC numbers: Primary 39A14, 32H30, 32A20

Supported by: This work was financially supported by the National Natural Science Foundation of China (Grant Nos.12171050, 12101068, 12071047).