Abstract
In this paper, we mainly investigate the value distribution of meromorphic functions in ℂm with its partial differential and uniqueness problem on meromorphic functions in ℂm 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.
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This work was partially supported by the NSFC (11271227, 11271161), the PCSIRT (IRT1264) and the Fundamental Research Funds of Shandong University (2017JC019).
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Liu, M., Gao, L. & Fang, S. Some Results Regarding Partial Differential Polynomials and the Uniqueness of Meromorphic Functions in Several Variables. Acta Math Sci 43, 821–838 (2023). https://doi.org/10.1007/s10473-023-0218-0
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DOI: https://doi.org/10.1007/s10473-023-0218-0
Key words
- meromorphic function in several variables
- Nevanlinna theory
- partial differential equation
- total derivative