By using the Nevanlinna's value distribution theory, this dissertation studies the problems of the uniqueness of meromorphic functions in four aspects, and several unicity theorems are obtained. In this dissertation, we study the uniqueness of entire functions sharing one value with its weight, and the uniqueness of entire functions concerning differential polynomials, and the uniqueness of meromorphic functions sharing two common range sets, and the uniqueness of meromorphic functions sharing one common range set. The results obtained in this dissertation perfect and generalize the present conclusions.
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