• Title, Summary, Keyword: meromorphic solution

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VALUE SHARING AND UNIQUENESS FOR THE POWER OF P-ADIC MEROMORPHIC FUNCTIONS

  • MENG, CHAO;LIU, GANG;ZHAO, LIANG
    • Journal of applied mathematics & informatics
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    • v.36 no.1_2
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    • pp.39-50
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    • 2018
  • In this paper, we deal with the uniqueness problem for the power of p-adic meromorphic functions. The results obtained in this paper are the p-adic analogues and supplements of the theorems given by Yang and Zhang [Non-existence of meromorphic solution of a Fermat type functional equation, Aequationes Math. 76(2008), 140-150], Chen, Chen and Li [Uniqueness of difference operators of meromorphic functions, J. Ineq. Appl. 2012(2012), Art 48], Zhang [Value distribution and shared sets of differences of meromorphic functions, J. Math. Anal. Appl. 367(2010), 401-408].

UNIQUENESS OF TWO DIFFERENTIAL POLYNOMIALS OF A MEROMORPHIC FUNCTION SHARING A SET

  • Ahamed, Molla Basir
    • Communications of the Korean Mathematical Society
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    • v.33 no.4
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    • pp.1181-1203
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    • 2018
  • In this paper, we are mainly devoted to find out the general meromorphic solution of some specific type of differential equation. We have also answered an open question posed by Banerjee-Chakraborty [4] by extending their results in a large extent. We have provided an example showing that the conclusion of the results of Zhang-Yang [16] is not general true. Some examples have been exhibited to show that certain claims are true in our main result. Finally some questions have been posed for the future research in this direction.

A NOTE ON MEROMORPHIC SOLUTIONS OF COMPLEX DIFFERENTIAL-DIFFERENCE EQUATIONS

  • Qi, Xiaoguang;Yang, Lianzhong
    • Bulletin of the Korean Mathematical Society
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    • v.56 no.3
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    • pp.597-607
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    • 2019
  • In this article, we consider properties of transcendental meromorphic solutions of the complex differential-difference equation $$P_n(z)f^{(n)}(2+{\eta}_n)+{\cdots}+P_1(z)f^{\prime}(z+{\eta}_1)+P_0(z)f(z+{\eta}_0)=0$$, and its non-homogeneous equation. Our results extend earlier results by Liu et al. [9].

ZEROS OF SOLUTIONS OF SECOND ORDER LINEAR DIFFERENTIAL EQUATIONS WITH COEFFICIENTS OF SMALL LOWER GROWTH

  • Wang, Sheng
    • Bulletin of the Korean Mathematical Society
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    • v.40 no.2
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    • pp.235-241
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    • 2003
  • It is proved that the product of any two linearly independent meromorphic solutions of second order linear differential equations with coefficients of small lower growth must have infinite exponent of convergence of its zero-sequences, under some suitable conditions.

MEROMORPHIC SOLUTIONS OF A COMPLEX DIFFERENCE EQUATION OF MALMQUIST TYPE

  • Zhang, Ran-Ran;Huang, Zhi-Bo
    • Bulletin of the Korean Mathematical Society
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    • v.51 no.6
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    • pp.1735-1748
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    • 2014
  • In this paper, we investigate the finite order transcendental meromorphic solutions of complex difference equation of Malmquist type $$\prod_{i=1}^{n}f(z+c_i)=R(z,f)$$, where $c_1,{\ldots},c_n{\in}\mathbb{C}{\backslash}\{0\}$, and R(z, f) is an irreducible rational function in f(z) with meromorphic coefficients. We obtain some results on deficiencies of the solutions. Using these results, we prove that the growth order of the finite order solution f(z) is 1, if f(z) has Borel exceptional values $a({\in}\mathbb{C})$ and ${\infty}$. Moreover, we give the forms of f(z).

SOME RESULTS ON UNIQUENESS OF MEROMORPHIC SOLUTIONS OF DIFFERENCE EQUATIONS

  • Gao, Zong Sheng;Wang, Xiao Ming
    • Communications of the Korean Mathematical Society
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    • v.32 no.4
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    • pp.959-970
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    • 2017
  • In this paper, we investigate the transcendental meromorphic solutions with finite order of two different types of difference equations $${\sum\limits_{j=1}^{n}}a_jf(z+c_j)={\frac{P(z,f)}{Q(z,f)}}={\frac{{\sum_{k=0}^{p}}b_kf^k}{{\sum_{l=0}^{q}}d_lf^l}}$$ and $${\prod\limits_{j=1}^{n}}f(z+c_j)={\frac{P(z,f)}{Q(z,f)}={\frac{{\sum_{k=0}^{p}}b_kf^k}{{\sum_{l=0}^{q}}d_lf^l}}$$ that share three distinct values with another meromorphic function. Here $a_j$, $b_k$, $d_l$ are small functions of f and $a_j{\not{\equiv}}(j=1,2,{\ldots},n)$, $b_p{\not{\equiv}}0$, $d_q{\not{\equiv}}0$. $c_j{\neq}0$ are pairwise distinct constants. p, q, n are non-negative integers. P(z, f) and Q(z, f) are two mutually prime polynomials in f.