On some properties of ultrametric meromorphic solutions of difference equations of Malmquist type

Let $\mathbb{K}$ be a complete ultrametric algebraically closed field of characteristic zero and let $\mathcal{M}(\mathbb{K})$ be the field of meromorphic functions in all $\mathbb{K}$. In this paper, using the ultrametric Nevanlinna theory, we investigate the growth of transcendental meromorphic solutions of some ultrametric difference equations. These difference equations arise from the analogue study of the differential equation of Malmquist type. We also give some characterizations of the order of growth for transcendental meromorphic solutions of such equations.