本文中, 我们利用多复变对数导数引理将Milloux不等式推广至关于整函数全导数的微分多项式. 作为应用, 我们证明了两个多复变 Picard 型定理: 设 $ f $ 是 $ \mathbb{C}^{n} $ 上的一个整函数, $ a, b $ 是两个判别复数且 $ b\neq 0, $ (1) 如果 $ f\neq a, $ $ f $ 关于全导数的微分多项式 $ {\cal{P}}\neq b, $ 则 $ f $ 是常函数; (2) 如果 $f^{s}D^{t_{1}}(f^{s_{1}})\cdots D^{t_{q}}(f^{s_{q}})\neq $ $ b,$ 且 $ s+\sum_{j = 1}^{q}s_{j}\geqslant 2+\sum_{j = 1}^{q}t_{j}, $ 则 $ f $ 是常函数, 其中 $ D^{k}f $ 是 $ f $ 的 $ k $ 阶全导数.

In this paper, we use the logarithmic derivative lemma for several complex variables to extend the Milloux inequality to differential polynomials of entire functions. As an application, we subsequently apply the concept to two Picard-type theorems: (1) Let $ f $ be an entire function in $\mathbb{C}^{n}$ and $a, b\;(\neq 0)$ be two distinct complex numbers. If $ f\neq a, {\cal{P}}\neq b, $ then $ f $ is constant. (2) If $ f^{s}D^{t_{1}}(f^{s_{1}})\cdots D^{t_{q}}(f^{s_{q}})\neq b $ and $ s+ $ $ \sum_{j = 1}^{q}s_{j}\geqslant 2+\sum_{j = 1}^{q}t_{j}, $ then $ f $ is constant, where $ D^{k}f $ is the $ k $ -th total derivative of $ f $ and $ {\cal{P}} $ is a differential polynomial of $ f $ with respect to the total derivative.