Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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ON SOLUTIONS TO SOME NONLINEAR DIFFERENCE AND DIFFERENTIAL EQUATIONS

  • Chen, Wei (Department of Mathematics Shandong University) ;
  • Hu, Pei-Chu (Department of Mathematics Shandong University) ;
  • Zhang, Yingying (School of Mathematical Sciences Xiamen University)
  • Received : 2015.05.14
  • Published : 2016.07.01
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Abstract

In this paper, we study entire solutions of some nonlinear difference equations and transcendental meromorphic solutons of some nonlinear differential equations. Our results generalize the results due to [11], [17].

Keywords

Acknowledgement

Supported by : Nature Science Foundation of China, PCSIRT

References

  1. Z. X. Chen, Growth and zeros of meromorphic solution of some linear difference equations, J. Math. Anal. Appl. 373 (2011), no. 1, 235-241. https://doi.org/10.1016/j.jmaa.2010.06.049
  2. Z. X. Chen, Zeros of entire solutions to complex linear difference equations, Acta Math. Sci. Ser. B Engl. Ed. 32 (2012), no. 3, 1141-1148.
  3. W. Cherry and Z. Ye, Nevanlinna's Theory of Value Distribution, Berlin-Heidelberg:Springer-Verlag, 2001.
  4. 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
  5. Y. M. Chiang and S. J. Feng, On the growth of logarithmic differences, difference quotients and logarithmic derivatives of meromorphic functions, Trans. Amer. Math. Soc. 361 (2009), no. 7, 3767-3791. https://doi.org/10.1090/S0002-9947-09-04663-7
  6. W. Hayman, Meromorphic Functions, Oxford: Clarendon Press, 1975.
  7. I. Laine, Nevanlinna Theory and Complex Differential Equations, Berlin-New York, Walter de Gruyter, 1993.
  8. B. Q. Li, On certain non-linear differential equations in complex domains, Arch. Math. (Basel) 91 (2008), no. 4, 344-353. https://doi.org/10.1007/s00013-008-2648-2
  9. K. Liu, Meromorphic functions sharing a set with applications to difference equations, J. Math. Anal. Appl. 359 (2009), no. 1, 384-393. https://doi.org/10.1016/j.jmaa.2009.05.061
  10. K. Liu, T. B. Cao, and H. Z. Cao, Entire solutions of Fermat type differential-difference equations, Arch. Math. (Basel) 99 (2012), no. 2, 147-155. https://doi.org/10.1007/s00013-012-0408-9
  11. K. Liu and L. Z. Yang, On entire solutions of some differential-difference equations, Comput. Methods Funct. Theory 13 (2013), no. 3, 433-447. https://doi.org/10.1007/s40315-013-0030-2
  12. P. Montel, Lecons sur les familles normales de fonctions analytiques et leurs applications, Gauthier-Villars, Paris, (1927), 135-136 (French).
  13. J. F. Tang and L. W. Liao, The transcendental meromorphic solutions of a certain type of nonlinear differential equations, J. Math. Anal. Appl. 334 (2007), no. 1, 517-527. https://doi.org/10.1016/j.jmaa.2006.12.075
  14. C. C. Yang, On entire solutions of a certain type of nonlinear differential equations, Bull. Aust. Math. Soc. 64 (2001), no. 3, 377-380. https://doi.org/10.1017/S0004972700019845
  15. C. C. Yang and P. Li, On the transcendental solutions of a certain type of nonlinear differential equations, Arch. Math. (Basel) 82 (2004), no. 5, 442-448. https://doi.org/10.1007/s00013-003-4796-8
  16. C. C. Yang and H. X. Yi, Uniqueness Theory of Meromorphic Functions, Kluwer Academic Publishers, Dordrecht, 2003.
  17. X. Zhang and L.W. Liao, On a certain type of nonlinear differential equations admitting transcendental meromorphic solutions, Sci. China Math. 56 (2013), no. 10, 2025-2034. https://doi.org/10.1007/s11425-013-4594-0

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