ON ENTIRE SOLUTIONS OF A CERTAIN TYPE OF NONLINEAR DIFFERENTIAL AND DIFFERENCE EQUATIONS

Abstract

In this paper, we investigate some analogous results on the existence of entire solutions of a certain type of nonlinear differential and differential-difference equations of the following form $$ f^n(z) + P_d(f) = p_1(z) e^{\alpha_1 z} + p_2(z) e^{\alpha_2 z},$$ where $P_d(f)$ is a differential polynomial or differential-difference polynomial in $f(z)$. And we find out its entire solutions or prove that it has no entire solution for some special $P_d(f)$.