On entire solutions of some type of nonlinear difference equations

In this article, the existence of finite order entire solutions of nonlinear difference equations $f^n+P_d\left(z,f\right)=p_1{e}^{{\alpha }_{1}z}+p_2{e}^{{\alpha }_{2}z}$ are studied, where n ≥ 2 is an integer, P_d(z, f) is a difference polynomial in f of degree d(≤ n ? 2), p₁, p₂ are small meromorphic functions of e^z, and α₁, α₂ are nonzero constants. Some necessary conditions are given to guarantee that the above equation has an entire solution of finite order. As its applications, we also find some type of nonlinear difference equations having no finite order entire solutions.