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Value distribution of meromorphic solutions of homogeneous and non-homogeneous complex linear differential-difference equations

100%
Luo L.-Q., Zheng X.-M.
Open Mathematics
|
2016
|
tom 14
|
nr 1
970-976
EN
In this paper, we investigate the value distribution of meromorphic solutions of homogeneous and non-homogeneous complex linear differential-difference equations, and obtain the results on the relations between the order of the solutions and the convergence exponents of the zeros, poles, a-points and small function value points of the solutions, which show the relations in the case of non-homogeneous equations are sharper than the ones in the case of homogeneous equations.
2
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Results on the deficiencies of some differential-difference polynomials of meromorphic functions

100%
Zheng X.-M., Xu H.-Y.
Open Mathematics
|
2016
|
tom 14
|
nr 1
100-108
EN
In this paper, we study the relation between the deficiencies concerning a meromorphic function f(z), its derivative f′(z) and differential-difference monomials f(z)mf(z+c)f′(z), f(z+c)nf′(z), f(z)mf(z+c). The main results of this paper are listed as follows: Let f(z) be a meromorphic function of finite order satisfying lim sup r→+∞ T(r, f) T(r,  f ′ ) <+∞, $$\mathop {\lim \,{\rm sup}}\limits_{r \to + \infty } {{T(r,\,f)} \over {T(r,\,f')}}{\rm{ < }} + \infty ,$$ and c be a non-zero complex constant, then δ(∞, f(z)m f(z+c)f′(z))≥δ(∞, f′) and δ(∞,f(z+c)nf′(z))≥ δ(∞, f′). We also investigate the value distribution of some differential-difference polynomials taking small function a(z) with respect to f(z).
3
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On meromorphic functions for sharing two sets and three sets inm-punctured complex plane

81%
Xu H.-Y., Zheng X.-M., Wang H.
Open Mathematics
|
2016
|
tom 14
|
nr 1
913-924
EN
In this article, we study the uniqueness problem of meromorphic functions in m-punctured complex plane Ω and obtain that there exist two sets S1, S2 with ♯S1 = 2 and ♯S2 = 9, such that any two admissible meromorphic functions f and g in Ω must be identical if f, g share S1, S2 I M in Ω.
4
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Some properties of solutions of complex q-shift difference equations

81%
Xu H.-Y., Tu J., Zheng X.-M.
Annales Polonici Mathematici
|
2013
|
tom 108
|
nr 3
289-304
EN
Combining difference and q-difference equations, we study the properties of meromorphic solutions of q-shift difference equations from the point of view of value distribution. We obtain lower bounds for the Nevanlinna lower order for meromorphic solutions of such equations. Our results improve and extend previous theorems by Zheng and Chen and by Liu and Qi. Some examples are also given to illustrate our results.
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