The authors consider meromorphic solutions of functional equations of the form
where the coefficients , are meromorphic functions and is a complex constant. If , then any local meromorphic solution around the origin has a meromorphic continuation over . The authors prove a number of results on the growth and value distribution of solutions of (1).
For a meromorphic function in the complex plane, let denote its Nevanlinna characteristic, and its order of growth. Furthermore, let , and . Then, for example, one of the results reads as follows.
Theorem. Let be a transcendental meromorphic solution of (1) with , and assume that . Then
Furthermore, the authors consider the special case
where , , , , , and is an entire function. They show that every meromorphic solution of (2) is entire, and they give a detailed analysis on the number of distinct meromorphic solutions.