About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 496096, 7 pages
http://dx.doi.org/10.1155/2013/496096
Research Article

Fixed Points of Meromorphic Solutions for Some Difference Equations

1School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China
2Department of Mathematics, College of Natural Sciences, Pusan National University, Pusan 609-735, Republic of Korea

Received 1 December 2012; Accepted 17 April 2013

Academic Editor: Patricia J. Y. Wong

Copyright © 2013 Zong-Xuan Chen and Kwang Ho Shon. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. W. K. Hayman, Meromorphic Functions, Oxford Mathematical Monographs, Clarendon Press, Oxford, UK, 1964. View at Zentralblatt MATH · View at MathSciNet
  2. I. Laine, Nevanlinna Theory and Complex Differential Equations, vol. 15 of de Gruyter Studies in Mathematics, Walter de Gruyter, Berlin, Germany, 1993. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. L. Yang, Value Distribution Theory, Science Press, Beijing, China, 1993. View at Zentralblatt MATH · View at MathSciNet
  4. M. J. Ablowitz, R. Halburd, and B. Herbst, “On the extension of the Painlevé property to difference equations,” Nonlinearity, vol. 13, no. 3, pp. 889–905, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. W. Bergweiler and J. K. Langley, “Zeros of differences of meromorphic functions,” Mathematical Proceedings of the Cambridge Philosophical Society, vol. 142, no. 1, pp. 133–147, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. B. Q. Chen, Z. X. Chen, and S. Li, “Uniqueness theorems on entire functions and their difference operators or shifts,” Abstract and Applied Analysis, vol. 2012, Article ID 906893, 8 pages, 2012. View at Publisher · View at Google Scholar
  7. Z. Chen, “On growth, zeros and poles of meromorphic solutions of linear and nonlinear difference equations,” Science China. Mathematics, vol. 54, no. 10, pp. 2123–2133, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. Z.-X. Chen and K. H. Shon, “On zeros and fixed points of differences of meromorphic functions,” Journal of Mathematical Analysis and Applications, vol. 344, no. 1, pp. 373–383, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. Z.-X. Chen and K. H. Shon, “Properties of differences of meromorphic functions,” Czechoslovak Mathematical Journal, vol. 61, no. 1, pp. 213–224, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. Y.-M. Chiang and S.-J. Feng, “On the Nevanlinna characteristic of f(z+η) and difference equations in the complex plane,” Ramanujan Journal, vol. 16, no. 1, pp. 105–129, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. Y.-M. Chiang and S.-J. Feng, “On the growth of logarithmic differences, difference quotients and logarithmic derivatives of meromorphic functions,” Transactions of the American Mathematical Society, vol. 361, no. 7, pp. 3767–3791, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. R. G. Halburd and R. J. Korhonen, “Difference analogue of the lemma on the logarithmic derivative with applications to difference equations,” Journal of Mathematical Analysis and Applications, vol. 314, no. 2, pp. 477–487, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. R. G. Halburd and R. J. Korhonen, “Existence of finite-order meromorphic solutions as a detector of integrability in difference equations,” Physica D, vol. 218, no. 2, pp. 191–203, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. R. G. Halburd and R. J. Korhonen, “Meromorphic solutions of difference equations, integrability and the discrete Painlevé equations,” Journal of Physics A, vol. 40, no. 6, pp. R1–R38, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. J. Heittokangas, R. Korhonen, I. Laine, J. Rieppo, and J. Zhang, “Value sharing results for shifts of meromorphic functions, and sufficient conditions for periodicity,” Journal of Mathematical Analysis and Applications, vol. 355, no. 1, pp. 352–363, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. J. Heittokangas, R. Korhonen, I. Laine, J. Rieppo, and K. Tohge, “Complex difference equations of Malmquist type,” Computational Methods and Function Theory, vol. 1, no. 1, pp. 27–39, 2001. View at Zentralblatt MATH · View at MathSciNet
  17. I. Laine and C.-C. Yang, “Clunie theorems for difference and q-difference polynomials,” Journal of the London Mathematical Society. Second Series, vol. 76, no. 3, pp. 556–566, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  18. S. Elaydi, An Introduction to Difference Equations, Undergraduate Texts in Mathematics, Springer, New York, NY, USA, 3rd edition, 2005. View at MathSciNet
  19. W. Bergweiler, “Proof of a conjecture of Gross concerning fix-points,” Mathematische Zeitschrift, vol. 204, no. 3, pp. 381–390, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. C.-T. Chuang and C.-C. Yang, Fix-Points and Factorization of Meromorphic Functions, World Scientific, Singapore, 1990. View at Publisher · View at Google Scholar · View at MathSciNet
  21. A. A. Gol'dberg and I. V. Ostrovskiĭ, The Distribution of Values of Meromorphic Functions, Nauka, Moscow, Russia, 1970. View at MathSciNet