The authors study some similarities between results on the existence and uniqueness of finite order entire solutions of nonlinear differential equations and difference-differential equations of the form
where is an integer, is a given non-vanishing meromorphic function of finite order, and is a linear difference-differential polynomials, with small meromorphic functions as coefficients.
The authors prove for example the following theorem:
Theorem 1. Let be polynomials. Then the nonlinear difference equation
has no transcendental entire solutions of finite order.