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Uniqueness and value-sharing of meromorphic functions. (English) Zbl 0890.30019
Concerning the uniqueness and sharing values of meromorphic functions, many results about meromorphic functions that share more than or equal to two values have been obtained. In this paper, we study meromorphic functions that share only one value, and prove the following result: For n11 and two meromorphic functions f(z) and g(z), if f n f ' and g n g ' share the same nonzero and finite value a with the same multiplicities, then fdg or g=c 1 e cz and f=c 2 e -cz , where d is an (n+1)th root of unity, c, c 1 and c 2 being constants. As applications, we solve some nonlinear differential equations.
Reviewer: X.Hua (Nanjing)

MSC:
30D35Distribution of values (one complex variable); Nevanlinna theory