On the Existence of Entire Solutions of Certain Class of Nonlinear Difference Equations

Abstract

In this paper, we study the existence and nonexistence of entire solutions of finite and infinite order of certain nonlinear difference equations of the form $$\begin{aligned} f^{n}\left( z\right) +L\left( z,f\right) =p_{1}\left( z\right) e^{\alpha _{1}\left( z\right) }+p_{2}\left( z\right) e^{\alpha _{2}\left( z\right) }, \quad \text { }n\ge 3 \end{aligned}$$ where \(p_{i}\left( z\right) \), \(\alpha _{i}\left( z\right) \)\(\left( i=1,2\right) \) are polynomials and \(L\left( z,f\right) \) is a nonzero linear difference polynomial in f, we give also an affirmative answer to the conjecture posed by Zhang et al. (Adv Differ Equ 2015:150, 2015).