Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2014, Article ID 378151, 12 pages
http://dx.doi.org/10.1155/2014/378151
Research Article

On the Deficiencies of Some Differential-Difference Polynomials

1Institute of Mathematics and Information Science, Jiangxi Normal University, Nanchang 330022, China
2Department of Informatics and Engineering, Jingdezhen Ceramic Institute, Jingdezhen 333403, China

Received 1 November 2013; Accepted 4 January 2014; Published 27 February 2014

Academic Editor: Zong-Xuan Chen

Copyright © 2014 Xiu-Min Zheng and Hong Yan Xu. 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, Clarendon Press, Oxford, UK, 1964.
  2. I. Laine, Nevanlinna Theory and Complex Differential Equations, Walter de Gruyter, Berlin, Germany, 1993. View at MathSciNet
  3. C. C. Yang and H. X. Yi, Uniqueness Theory of Meromorphic Functions, Kluwer Academic Publishers Group, Dordrecht, The Netherlands, 2003.
  4. 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 Scopus
  5. 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 Scopus
  6. R. G. Halburd, R. J. Korhonen, and K. Toghe, “Holomorphic curves with shift-invariant hyper-plane preimages,” Transactions of the American Mathematical Society. In press, http://arxiv.org/abs/0903.3236.
  7. 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 Scopus
  8. 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 MathSciNet · View at Scopus
  9. Z. X. Chen, “Complex oscillation of meromorphic solutions for the Pielou logistic equation,” Journal of Difference Equations and Applications, vol. 19, no. 11, pp. 1795–1806, 2013. View at Publisher · View at Google Scholar
  10. Z. X. Chen and K. H. Shon, “Fixed points of meromorphic solutions for some difference equations,” Abstract and Applied Analysis, vol. 2013, Article ID 496096, 7 pages, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  11. K. Ishizaki and N. Yanagihara, “Wiman-Valiron method for difference equations,” Nagoya Mathematical Journal, vol. 175, pp. 75–102, 2004. View at Google Scholar · View at MathSciNet · View at Scopus
  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 · View at Scopus
  13. I. Laine and C. C. Yang, “Value distribution of difference polynomials,” Proceedings of the Japan Academy A, vol. 83, no. 8, pp. 148–151, 2007. View at Google Scholar · View at MathSciNet
  14. C.-C. Yang and I. Laine, “On analogies between nonlinear difference and differential equations,” Proceedings of the Japan Academy A, vol. 86, no. 1, pp. 10–14, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  15. R. R. Zhang and Z. B. Huang, “Results on difference analogues of Valiron-Mokhon’ko theorem,” Abstract and Applied Analysis, vol. 2013, Article ID 273040, 6 pages, 2013. View at Google Scholar
  16. X. M. Zheng and Z. X. Chen, “On deficiencies of some difference polynomials,” Acta Mathematica Sinica, vol. 54, no. 6, pp. 983–992, 2011 (Chinese). View at Google Scholar
  17. X. M. Zheng and Z. X. Chen, “On the value distribution of some difference polynomials,” Journal of Mathematical Analysis and Applications, vol. 397, no. 2, pp. 814–821, 2013. View at Google Scholar
  18. G. Valiron, “Sur la dérivée des fonctions algébroides,” Bulletin de la Société Mathématique de France, vol. 59, pp. 17–39, 1931. View at Google Scholar
  19. A. Z. Mokhon’ko and V. D. Mokhon’ko, “Estimates of the Nevanlinna characteristics of certain classes of meromorphic functions and their applications to differential equations,” Sibirskii Matematicheskii Zhurnal, vol. 15, pp. 1305–1322, 1974 (Russian). View at Google Scholar · View at MathSciNet
  20. W. K. Hayman, “Picard values of meromorphic functions and their derivatives,” Annals of Mathematics, vol. 70, no. 2, pp. 9–42, 1959. View at Google Scholar · View at MathSciNet
  21. C.-C. Yang, “On deficiencies of differential polynomials,” Mathematische Zeitschrift, vol. 116, no. 3, pp. 197–204, 1970. View at Publisher · View at Google Scholar · View at Scopus
  22. C.-C. Yang, “On deficiencies of differential polynomials, II,” Mathematische Zeitschrift, vol. 125, no. 2, pp. 107–112, 1972. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  23. A. A. Gol’dberg and I. V. Ostrovskii, The Distribution of Values of Meromorphic Functions, Nauka, Moscow, Russia, 1970, (Russian).
  24. E. Mues and N. Steinmetz, “The theorem of Tumura-Clunie for meromorphic functions,” Journal of the London Mathematical Society, vol. 23, no. 2, pp. 113–122, 1981. View at Google Scholar · View at MathSciNet