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

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 $P_d(f)$.