SOME RESULTS REGARDING PARTIAL DIFFERENTIAL POLYNOMIALS AND THE UNIQUENESS OF MEROMORPHIC FUNCTIONS IN SEVERAL VARIABLES*

doi:10.1007/s10473-023-0218-0

Acta mathematica scientia,Series B ›› 2023, Vol. 43 ›› Issue (2): 821-838.doi: 10.1007/s10473-023-0218-0

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SOME RESULTS REGARDING PARTIAL DIFFERENTIAL POLYNOMIALS AND THE UNIQUENESS OF MEROMORPHIC FUNCTIONS IN SEVERAL VARIABLES^*

Manli Liu¹, Lingyun Gao^2,†, Shaomei Fang¹

1. Department of Mathematics, South China Agricultural University, Guangzhou 510642, China;
2. Department of Mathematics, Jinan University, Guangzhou 510632, China

Received:2021-10-06 Revised:2022-03-01 Online:2023-03-25 Published:2023-04-12
Contact: †Lingyun GAO, E-mail: tgaoly@jnu.edu.cn.
About author:Manli Liu, E-mail: lml6641@163.com; Shaomei Fang, E-mail: dz90@scau.edu.cn
Supported by:
This work was partially supported by the NSFC (11271227, 11271161), the PCSIRT (IRT1264) and the Fundamental Research Funds of Shandong University (2017JC019).

Abstract

Abstract: In this paper, we mainly investigate the value distribution of meromorphic functions in $\mathbb{C}^m$ with its partial differential and uniqueness problem on meromorphic functions in $\mathbb{C}^m$ and with its $k$ -th total derivative sharing small functions. As an application of the value distribution result, we study the defect relation of a nonconstant solution to the partial differential equation. In particular, we give a connection between the Picard type theorem of Milliox-Hayman and the characterization of entire solutions of a partial differential equation.

Key words: meromorphic function in several variables, Nevanlinna theory, partial differential equation, total derivative

Manli Liu, Lingyun Gao, Shaomei Fang. SOME RESULTS REGARDING PARTIAL DIFFERENTIAL POLYNOMIALS AND THE UNIQUENESS OF MEROMORPHIC FUNCTIONS IN SEVERAL VARIABLES^*[J].Acta mathematica scientia,Series B, 2023, 43(2): 821-838.

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SOME RESULTS REGARDING PARTIAL DIFFERENTIAL POLYNOMIALS AND THE UNIQUENESS OF MEROMORPHIC FUNCTIONS IN SEVERAL VARIABLES^*

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