On existence of meromorphic solutions for certain
q-difference equation
Changwen Penga, Zongxuan Chenb, Huawei Huangc,*, Lei Taoc
ABSTRACT: We consider the existence of transcendental meromorphic solutions of q-difference equation
Xn
j=1
cj
(z)f (q
j
z) = P(z, f (z))
Q(z, f (z)),
where P(z, f (z)) and Q(z, f (z)) are polynomials in f having rational coefficients and no common roots, cj
(z) are
rational functions, q ? C and 0 < |q| ? 1. We obtain that such equation has no transcendental meromorphic solutions
for the case m = degf P ? degf Q ? 2.