数学物理学报(英文版) ›› 2023, Vol. 43 ›› Issue (2): 821-838.doi: 10.1007/s10473-023-0218-0
Manli Liu1, Lingyun Gao2,†, Shaomei Fang1
Manli Liu1, Lingyun Gao2,†, Shaomei Fang1
摘要: 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.