On the meromorphic solutions of a certain type of nonlinear difference-differential equation

Abstract

. The main objective of this paper is to give the specific forms of the meromorphic solutions of the nonlinear difference-differential equation where P d ( z, f ) is a difference-differential polynomial in f ( z ) of degree d 6 n − 1 with small functions of f ( z ) as its coefficients, p 1 , p 2 are nonzero rational functions and α 1 , α 2 are non-constant polynomials. More precisely, we find out the conditions for ensuring the existence of meromorphic solutions of the above equation.