On the functional equation \(P(f)=Q(g)\) in non-Archimedean field
The author finds conditions on nonlinear polynomials \(P\) and \(Q\) over a complete non-Archimedean field \(K\), under which no non-constant meromorphic functions \(f,g\) on \(K\) can satisfy the functional equation \(P(f)=Q(g)\). For some related results regarding, in particular, meromorphic solutions on a disk, see \textit{A. Escassut} and \textit{C.-C. Yang} [J. Number Theory 105, No. 2, 344--360 (2004; Zbl 1054.30043)].
scientific article; zbMATH DE number 5122047