On analogies between nonlinear difference and differential equations

Abstract

In this paper, we point out some similarities between results on the existence and uniqueness of finite order entire solutions of the nonlinear differential equations and differential-difference equations of the form $$f^n+L(z,f)=h.$$ Here n is an integer $\geq 2$, h is a given non-vanishing meromorphic function of finite order, and L(z,f) is a linear differential-difference polynomial, with small meromorphic functions as the coefficients.