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We establish some uniqueness results for meromorphic functions when two nonlinear differential polynomials P (f) k ∏ i=1 (f )i and P (g) k ∏ i=1 (g)i share a nonzero polynomial with certain degree and our results improve and generalize some recent results in Y.-H.Cao, X.-B. Zhang (2012). Also we exhibit two examples to show that the conditions used in the results are sharp.

Generalizations on the results of Cao and Zhang