Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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ON UNICITY OF MEROMORPHIC SOLUTIONS OF DIFFERENTIAL-DIFFERENCE EQUATIONS

  • Received : 2017.06.05
  • Accepted : 2017.09.05
  • Published : 2018.07.01
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Abstract

In this paper, we give a uniqueness theorem on meromorphic solutions f of finite order of a class of differential-difference equations such that solutions f are uniquely determined by their poles and two distinct values.

Keywords

Acknowledgement

Supported by : NSFC of China, PCSIRT

References

  1. G. Brosch, Eindeutigkeitssatze fur meromorphe funktionen, Dissertation, Technical University of Aachen, 1989.
  2. Y.-M. Chiang and S.-J. Feng, On the Nevanlinna characteristic of f(z+${\eta}$) and difference equations in the complex plane, Ramanujan J. 16 (2008), no. 1, 105-129. https://doi.org/10.1007/s11139-007-9101-1
  3. H. Li, On existence of solutions of differential-difference equations, Math. Methods Appl. Sci. 39 (2016), no. 1, 144-151. https://doi.org/10.1002/mma.3465
  4. I. Laine, Nevanlinna theory and complex differential equations, De Gruyter Studies in Mathematics, 15, Walter de Gruyter & Co., Berlin, 1993.
  5. F. Lu, Q. Han, and W. Lu, On unicity of meromorphic solutions to difference equations of Malmquist type, Bull. Aust. Math. Soc. 93 (2016), no. 1, 92-98. https://doi.org/10.1017/S0004972715000787
  6. Z. H. Tu, Some Malmquist-type theorems of partial differential equations on $C^n$, J. Math. Anal. Appl. 179 (1993), no. 1, 41-60. https://doi.org/10.1006/jmaa.1993.1334
  7. C. Yang, On entire solutions of a certain type of nonlinear differential equation, Bull. Austral. Math. Soc. 64 (2001), no. 3, 377-380. https://doi.org/10.1017/S0004972700019845
  8. C.-C. Yang and H.-X. Yi, Uniqueness theory of meromorphic functions, Mathematics and its Applications, 557, Kluwer Academic Publishers Group, Dordrecht, 2003.