Unicity of meromorphic functions related to their derivatives

Abstract

In this paper, we shall study the unicity of meromorphic functions defined over non-Archimedean fields of characteristic zero such that their valence functions of poles grow slower than their characteristic functions. If $f$ is such a function, and $f$ and a linear differential polynomial $P(f)$ of $f$, whose coefficients are meromorphic functions growing slower than $f$, share one finite value $a$ CM, and share another finite value $b\ (\not=a)$ IM, then $P(f)=f$.