摘要：In this paper, we consider the q-difference analogue of the Clunie theorem. We obtain there is no zero-order entire solution of f n ( z ) + ( ∇ q f ( z ) ) n = 1 when n ≥ 2 ; there is no zero-order transcendental entire solution of f n ( z ) + P ( z ) ( ∇ q f ( z ) ) m = Q ( z ) when n > m ≥ 0 ; and the equation f n + P ( z ) ∇ q f ( z ) = h ( z ) has at most one zero-order transcendental entire solution f if f is not the solution of ∇ q f ( z ) = 0 , when n ≥ 4 . MSC:30D35, 30D30, 39A13, 39B12.
关键词：uniqueness ; q -shift ; q -difference equations ; entire functions ; zero order ; Nevanlinna theory
