  Two purposes will be shown in this paper. The first one is to extend the
classic Tumura-Clunie type theorem for meromorphic functions of one complex
variable to meromorphic functions of several complex variables by using Clunie
lemma. The second one is to characterize entire solutions of certain partial
differential equations in $\mathbb{C}^{m}$. Our results are extensions and
generalizations of the previous theorems by Liao-Ye \cite{Liao-Ye} and Li
\cite{Li11}.
