Meromorphic solutions of a certain type of nonlinear differential equation

Our paper focuses on investigating the existence and possible forms of solutions to the nonlinear differential equation f^m+(Rf⁽ᵏ⁾)^n=Qe^α, where where k, m and n are three positive integers, Q and R are non-zero rational functions, and $α$ is a polynomial. We examine this equation systematically for all positive integral values of k, m and n, providing comprehensive conditions under which entire or meromorphic solutions may exist. Our results offer substantial improvements over those of Tang and Liao {TL1} and Han and Lü {HL1}, particularly with respect to the existence criteria and the explicit analytic forms of admissible solutions. These findings contribute meaningfully to the broader study of nonlinear differential polynomials and Fermat-type functional equations in complex analysis.