**Authors: **Zhi Tao Wen Janne Heittokangas Ilpo Lain

**Publish Date**: 2012/01/19

**Volume:** 28, **Issue:** 7, **Pages:** 1295-1306

## Abstract

Recently CC Yang and I Laine have investigated finite order entire solutions f of nonlinear differentialdifference equations of the form f n + Lz f = h where n ≥ 2 is an integer In particular it is known that the equation fz2 +qzfz +1 = pz where pzqz are polynomials has no transcendental entire solutions of finite order Assuming that Qz is also a polynomial and c ∈ ℂ equations of the form fz n +qzeQz fz +c = pz do posses finite order entire solutions A classification of these solutions in terms of growth and zero distribution will be given In particular it is shown that any exponential polynomial solution must reduce to a rather specific form This reasoning relies on an earlier paper due to N Steinmetz

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