Existence of zero-order meromorphic solutions of certain q-difference equations
Existence of zero-order meromorphic solutions of certain q-difference equations
In this paper, we consider the q-difference equation (f(qz)+f(z))(f(z)+f(z/q))=R(z,f), where R(z,f) is rational in f and meromorphic in z. It shows that if the above equation assumes an admissible zero-order meromorphic solution f(z) , then either f(z) is a solution of a q-difference Riccati equation or the coefficients satisfy some …