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      Uniqueness of meromorphic solutions of a certain type of difference equations

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      https://www.riss.kr/link?id=A108211414

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      다국어 초록 (Multilingual Abstract)

      In this paper, we study the uniqueness of two finite order transcendental meromorphic solutions $f(z)$ and $g(z)$ of the following complex difference equation $$A_{1}(z)f(z+1)+A_{0}(z)f(z)=F(z)e^{\alpha(z)}$$ when they share 0, $\infty$ CM, where $A_{...

      In this paper, we study the uniqueness of two finite order transcendental meromorphic solutions $f(z)$ and $g(z)$ of the following complex difference equation $$A_{1}(z)f(z+1)+A_{0}(z)f(z)=F(z)e^{\alpha(z)}$$ when they share 0, $\infty$ CM, where $A_{1}(z),$ $A_{0}(z),$ $F(z)$ are non-zero polynomials, $\alpha(z)$ is a polynomial. Our result generalizes and complements some known results given recently by Cui and Chen, Li and Chen. Examples for the precision of our result are also supplied.

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      참고문헌 (Reference)

      1 Sheng Li, "Uniqueness of meromorphic solutions of the difference equation R1(z)f(z + 1) + R2(z)f(z) = R3(z)" Springer Science and Business Media LLC 2019 (2019): 2019

      2 J. Heittokangas, "Uniqueness of meromorphic functions sharing values with their shifts" 56 (56): 81-92, 2011

      3 X. Qi, "Uniqueness of meromorphic functions concerning their differences and solutions of difference Painlev´e equations" 18 (18): 567-582, 2018

      4 N. Cui, "Uniqueness for meromorphic solutions sharing three values with a meromorphic function to some linear difference equations" 38 (38): 13-22, 2017

      5 C. -C. Yang, "Uniqueness Theory of Meromorphic Functions, Mathematics and its Applications" Kluwer Academic Publishers Group 2003

      6 N. Cui, "Unicity for meromorphic solutions of some difference equations sharing three values of any meromorphic function" 48 (48): 83-87, 2016

      7 F. Lu, "On unicity of meromorphic solutions to difference equations of Malmquist type" 93 (93): 92-98, 2016

      8 Y. -M. Chiang, "On the Nevanlinna characteristic of f(z+η)and difference equations in the complex plane" 16 (16): 105-129, 2008

      9 Z. -X. Chen, "On sharing values of meromorphic functions and their differences" 63 (63): 557-565, 2013

      10 Zong-Xuan Chen, "On Growth of Meromorphic Solutions for Linear Difference Equations" Hindawi Limited 2013 : 1-6, 2013

      1 Sheng Li, "Uniqueness of meromorphic solutions of the difference equation R1(z)f(z + 1) + R2(z)f(z) = R3(z)" Springer Science and Business Media LLC 2019 (2019): 2019

      2 J. Heittokangas, "Uniqueness of meromorphic functions sharing values with their shifts" 56 (56): 81-92, 2011

      3 X. Qi, "Uniqueness of meromorphic functions concerning their differences and solutions of difference Painlev´e equations" 18 (18): 567-582, 2018

      4 N. Cui, "Uniqueness for meromorphic solutions sharing three values with a meromorphic function to some linear difference equations" 38 (38): 13-22, 2017

      5 C. -C. Yang, "Uniqueness Theory of Meromorphic Functions, Mathematics and its Applications" Kluwer Academic Publishers Group 2003

      6 N. Cui, "Unicity for meromorphic solutions of some difference equations sharing three values of any meromorphic function" 48 (48): 83-87, 2016

      7 F. Lu, "On unicity of meromorphic solutions to difference equations of Malmquist type" 93 (93): 92-98, 2016

      8 Y. -M. Chiang, "On the Nevanlinna characteristic of f(z+η)and difference equations in the complex plane" 16 (16): 105-129, 2008

      9 Z. -X. Chen, "On sharing values of meromorphic functions and their differences" 63 (63): 557-565, 2013

      10 Zong-Xuan Chen, "On Growth of Meromorphic Solutions for Linear Difference Equations" Hindawi Limited 2013 : 1-6, 2013

      11 I. Laine, "Nevanlinna Theory and Complex Differential Equations, De Gruyter Studies in Mathematics" Walter de Gruyter & Co 1993

      12 N. Yanagihara, "Meromorphic solutions of some difference equations" 23 (23): 309-326, 1980

      13 Xiao-Min Li ; Hong-Xun Yi, "Meromorphic functions sharing four values with their difference operators or shifts" 대한수학회 53 (53): 1213-1235, 2016

      14 W. K. Hayman, "Meromorphic Functions, Oxford Mathematical Monographs" Clarendon Press 1964

      15 R. Nevanlinna, "Le theoreme de Picard-Borel et la theorie des fonctions meromorphes" Chelsea Publishing Co 1974

      16 S. Shimomura, "Entire solutions of a polynomial difference equation" 28 (28): 253-266, 1981

      17 R. G. Halburd, "Difference analogue of the lemma on the logarithmic derivative with applications to difference equations" 314 (314): 477-487, 2006

      18 Z. X. Chen, "Complex Differences and Difference Equations" Science Press 2014

      19 S. B. Bank, "An extension of Holder’s theorem concerning the gamma function" 19 (19): 53-63, 1976

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      2023 평가예정 해외DB학술지평가 신청대상 (해외등재 학술지 평가)
      2020-01-01 평가 등재학술지 유지 (해외등재 학술지 평가) KCI등재
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      2001-07-01 평가 등재학술지 선정 (등재후보2차) KCI등재
      1999-01-01 평가 등재후보학술지 선정 (신규평가) KCI등재후보
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      기준연도 WOS-KCI 통합IF(2년) KCIF(2년) KCIF(3년)
      2016 0.35 0.1 0.27
      KCIF(4년) KCIF(5년) 중심성지수(3년) 즉시성지수
      0.23 0.2 0.339 0.04
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