Crossing Malmquist Systems with Certain Types

Abstract

In this paper, we will present the expression of meromorphic solutions on the crossing differential or difference Malmquist systems of certain types using Nevanlinna theory. For instance, we consider the admissible meromorphic solutions of the crossing differential Malmquist system

$$\begin{cases}f^{\prime}_{1}(z)=\frac{a_{1}(z)f_{2}(z)+a_{0}(z)}{f_{2}(z)+d_{1}(z)},\\ f^{\prime}_{2}(z)=\frac{a_{2}(z)f_{1}(z)+b_{0}(z)}{f_{1}(z)+d_{2}(z)},\end{cases}$$

where \(a_{1}(z)d_{1}(z)\not\equiv a_{0}(z)\) and \(a_{2}(z)d_{2}(z)\not\equiv b_{0}(z)\).