On meromorphic solutions of some algebraic partial differential equations on \(C^n\) (Q1378653)

Applying the techniques from Nevanlinna theory of value distribution theory of the meromorphic functions on \(\mathbb{C}^n\), the author investigates the existence problem of meromorphic solutions and obtaines a satisfactory Malmquist type theorem for a class of algebraic partial differential equations on \(\mathbb{C}^n\) which improves some earlier main results. It is very easy to generalize the results in this paper to the general case of higher-order algebraic partial differential equation on \(\mathbb{C}^n\) by the same techniques.