Entire Solutions of a Certain Type of Nonlinear Differential-Difference Equations

Abstract

The aim of the paper is to investigate all transcendental entire solutions of the following general nonlinear equation of the form \(f^{n}+P_{d}(z,f)=p_{1}e^{\alpha _{1}z}+p_{2}e^{\alpha _{2}z}\), where P_d(z,f) is a differential-difference polynomial in f of degree d. Our result is a generalization and complement of known results obtained by Liu-Mao, L\({\ddot {\mathrm {u}}}\) et al. and the references therein.