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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 306360, 5 pages
http://dx.doi.org/10.1155/2014/306360
Research Article

Admissible Solutions of the Schwarzian Type Difference Equation

College of Science, Guangdong Ocean University, Zhanjiang 524088, China

Received 14 January 2014; Accepted 20 March 2014; Published 7 April 2014

Academic Editor: Zong-Xuan Chen

Copyright © 2014 Baoqin Chen and Sheng Li. 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 MathSciNet
  2. I. Laine, Nevanlinna Theory and Complex Differential Equations, Walter de Gruyter, Berlin, Germany, 1993. View at Publisher · View at Google Scholar · View at MathSciNet
  3. C.-C. Yang and H.-X. Yi, Uniqueness Theory of Meromorphic Functions, vol. 557 of Mathematics and Its Applications, Kluwer Academic Publishers Group, Dordrecht, The Netherlands, 2003. 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. 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
  7. 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
  8. 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
  9. R. G. Halburd and R. J. Korhonen, “Existence of finite-order meromorphic solutions as a detector of integrability in difference equations,” Physica D: Nonlinear Phenomena, vol. 218, no. 2, pp. 191–203, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. R. G. Halburd, R. J. Korhonen, and K. Tohge, “Holomorphic curves with shift-invariant hyperplane preimages,” submitted to Transactions of the American Mathematical Society, http://arxiv.org/abs/0903.3236.
  11. 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 Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. I. Laine and C.-C. Yang, “Clunie theorems for difference and q-difference polynomials,” Journal of the London Mathematical Society, vol. 76, no. 3, pp. 556–566, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  13. K. Ishizaki, “Admissible solutions of the Schwarzian differential equation,” Australian Mathematical Society A: Pure Mathematics and Statistics, vol. 50, no. 2, pp. 258–278, 1991. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. A. Z. Mohon'ko, “The nevanlinna characteristics of certain meromorphic functions,” Teorija Funkciĭ, Funkcional'nyĭ Analiz i ih Priloženija, no. 14, pp. 83–87, 1971 (Russian). View at Google Scholar · View at MathSciNet
  15. G. Valiron, “Sur la dérivée des fonctions algébroides,” Bulletin de la Société Entomologique de France, vol. 59, pp. 17–39, 1931. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. G. Jank and L. Volkmann, Meromorphe Funktionen und Differentialgeichungen, Birkhäuser Verlag, Basel, Switzerland, 1985.