Solutions of nonlinear difference equations

The non-vanishing finite order entire solutions of nonlinear difference equationf(z)n+an−1f(z)n−1+⋯+a1f(z)+q(z)eQ(z)f(z+c)=P(z), are studied in this paper for n≥2 and n=1, respectively, where q(z), Q(z), P(z) are polynomials and an−1,…,a1,c∈C. We classified these solutions according to growth and zero distribution. Particularly, we show that exponential polynomial solutions satisfying certain conditions must reduce to rather specific forms when n=2 and a1≠0. Our results are improvements and complements of Wen et al. [13].