Some Malmquist-Type Theorems of Partial Differential Equations on Cn

In this paper, using the techniques and some basic results from the value distribution theory in several complex variables, we investigate the existence problem of meromorphic solutions of a class of partial differential equations on Cn. Some Malmquist type theorems of partial differential equations on Cn are established. A Rellich-type theorem of partial differential equations on Cn is also obtained. Several examples are given to complement the theory.