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Uniqueness of meromorphic functions sharing a meromorphic function of a smaller order with their derivatives

100%
Li X.-M., Yi H.-X.
Annales Polonici Mathematici
|
2010
|
tom 98
|
nr 3
207-219
EN
We prove some uniqueness theorems for meromorphic functions and their derivatives that share a meromorphic function whose order is less than those of the above meromorphic functions. The results in this paper improve those given by G. G. Gundersen & L. Z. Yang, J. P. Wang, J. M. Chang & Y. Z. Zhu, and others. Some examples are provided to show that our results are the best possible.
2
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Results on weighted sharing of values for meromorphic functions

100%
Li X.-M., Yi H.-X.
Annales Polonici Mathematici
|
2007
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tom 92
|
nr 1
55-67
EN
We prove some results on uniqueness of functions with three shared values. Our results improve those given by H. X. Yi, I. Lahiri, T. C. Alzahary & H. X. Yi, and other authors.
3
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On uniqueness of meromorphic functions sharing three values and a set consisting of two small meromorphic functions

100%
Li X.-M., Yi H.-X.
Annales Polonici Mathematici
|
2009
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tom 96
|
nr 1
1-23
EN
We deal with a uniqueness theorem of two meromorphic functions that share three values with weights and also share a set consisting of two small meromorphic functions. Our results improve those by G. Brosch, I. Lahiri & P. Sahoo, T. C. Alzahary & H. X. Yi, P. Li & C. C. Yang, and others.
4
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On a kth-order differential equation

100%
Li X.-M., Gao C.-C.
Annales Polonici Mathematici
|
2006
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tom 89
|
nr 1
53-63
EN
We prove a theorem on the growth of a solution of a kth-order linear differential equation. From this we obtain some uniqueness theorems. Our results improve several known results. Some examples show that the results are best possible.
5
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Uniqueness theorems for entire functions whose difference polynomials share a meromorphic function of a smaller order

81%
Li X.-M., Li W.-L., Yi H.-X., Wen Z.-T.
Annales Polonici Mathematici
|
2011
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tom 102
|
nr 2
111-127
EN
We deal with uniqueness of entire functions whose difference polynomials share a nonzero polynomial CM, which corresponds to Theorem 2 of I. Laine and C. C. Yang [Proc. Japan Acad. Ser. A 83 (2007), 148-151] and Theorem 1.2 of K. Liu and L. Z. Yang [Arch. Math. 92 (2009), 270-278]. We also deal with uniqueness of entire functions whose difference polynomials share a meromorphic function of a smaller order, improving Theorem 5 of J. L. Zhang [J. Math. Anal. Appl. 367 (2010), 401-408], where the entire functions are of finite orders.
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