Transcendental meromorphic solutions of certain nonlinear difference equations

Abstract

In this paper, we mainly explore the following finite order meromorphic solutions of the nonlinear difference equationfn(z)+Pd(z,f)=p1eα1zk+p2eα2zk, where n≥2, k≥1 are two integers, Pd(z,f) is a difference polynomial in f of degree d≤n−1 with polynomials as its coefficients, and pj, αj(j=1,2) are nonzero constants satisfying certain conditions. Furthermore, we obtain the exact forms of meromorphic solutions of the above difference equation. The result of this paper extends and improves previous results, and some examples are given to show the accuracy of the result.