摘要：In this paper, we investigate the existence and growth of solutions of the q-difference equation ∏ i = 1 n f ( q i z ) = R ( z , f ( z ) ) $\prod_{i=1}^{n}f(q_{i}z)=R(z,f(z))$ , where R ( z , f ( z ) ) $R(z,f(z))$ is an irreducible rational function in f ( z ) $f(z)$ . We also give an estimation of the growth of transcendental meromorphic solutions of the equation ∏ i = 1 n f ( q i z ) = f ( z ) m $\prod_{i=1}^{n}f(q_{i}z)=f(z)^{m}$ .
