Existence of meromorphic solutions of systems of partial differential-difference equations (Q2681263)

Nevanlinna theory and Wiman-Valiron theory play an important role in the study of complex differential and difference equations. By means of them, a large number of results for differential and difference equations in one complex variable were obtained. In recent years, the partial differential-difference equations in several complex variables have attracted more and more attention of researchers in this field. In this paper, the authors consider the existence of admissible meromorphic solutions of a certain type of systems of partial differential-difference equations in several complex variables. They obtain two main theorems and a technical lemma based on Nevanlinna theory. In particular, in Theorem 2 the authors prove a sufficient condition guaranteeing the existence of at least two admissible solutions for the considered system. This condition is then used in Theorem 1 and three examples are discussed to illustrate the theoretical results.