On the uniqueness problem of non-Archimedean meromorphic functions and their differential polynomials

Abstract. In this paper, we discuss the uniqueness problem for differential polynomials \((P^n(f))^{(k)}, (Q^n(g))^{(k)}\), sharing the same value, where \( P \), \( Q \) are polynomials of Fermat–Waring type, \(f\) and \(g\) are meromorphic functions on a non-Archimedean field.