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Discrete Dynamics in Nature and Society
Volume 2015, Article ID 723025, 10 pages
http://dx.doi.org/10.1155/2015/723025
Research Article

The Existence of Meromorphic Solutions of Some Types of Systems of Complex Functional Equations

1Department of Informatics and Engineering, Jingdezhen Ceramic Institute, Jingdezhen, Jiangxi 333403, China
2Jiangxi Normal University, Nanchang, Jiangxi 330027, China

Received 4 August 2015; Accepted 13 September 2015

Academic Editor: Chris Goodrich

Copyright © 2015 Hong-Yan Xu et al. 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. D. C. Barnett, R. G. Halburd, W. Morgan, and R. J. Korhonen, “Nevanlinna theory for the q-difference operator and meromorphic solutions of q-difference equations,” Proceedings of the Royal Society of Edinburgh Section A: Mathematics, vol. 137, no. 3, pp. 457–474, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  2. Y.-M. Chiang and S.-J. Feng, “On the Nevanlinna characteristic of f(z+η) and difference equations in the complex plane,” The Ramanujan Journal, vol. 16, no. 1, pp. 105–129, 2008. View at Publisher · View at Google Scholar
  3. 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 · View at Scopus
  4. Z. X. Chen, Z. B. Huang, and X. M. Zheng, “On properties of difference polynomials,” Acta Mathematica Scientia B, vol. 31, no. 2, pp. 627–633, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  5. R. G. Halburd and R. J. Korhonen, “Nevanlinna theory for the difference operator,” Annales Academiae Scientiarum Fennicae. Mathematica, vol. 31, no. 2, pp. 463–478, 2006. View at Google Scholar · View at MathSciNet
  6. 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 MathSciNet · View at Scopus
  7. I. Laine and C.-C. Yang, “Value distribution of difference polynomials,” Proceedings of the Japan Academy—Series A, Mathematical Sciences, vol. 83, no. 8, pp. 148–151, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. K. Liu and L.-Z. Yang, “Value distribution of the difference operator,” Archiv der Mathematik, vol. 92, no. 3, pp. 270–278, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  9. J. Zhang and R. Korhonen, “On the Nevanlinna characteristic of f(qz) and its applications,” Journal of Mathematical Analysis and Applications, vol. 369, no. 2, pp. 537–544, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  10. X.-M. Zheng and Z.-X. Chen, “Some properties of meromorphic solutions of q-difference equations,” Journal of Mathematical Analysis and Applications, vol. 361, no. 2, pp. 472–480, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. W. K. Hayman, Meromorphic Functions, Clarendon Press, Oxford, UK, 1964. View at MathSciNet
  12. L. Yang, Value Distribution Theory, Springer, Berlin, Germany, 1993. View at MathSciNet
  13. H. X. Yi and C. C. Yang, Uniqueness Theory of Meromorphic Functions, Kluwer Academic Publishers, Dordrecht, The Netherlands, 2003, Chinese Original: Science Press, Beijing, China, 1995.
  14. 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
  15. G. G. Gundersen, J. Heittokangas, I. Laine, J. Rieppo, and D. Yang, “Meromorphic solutions of generalized Schröder equations,” Aequationes Mathematicae, vol. 63, no. 1-2, pp. 110–135, 2002. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  16. X. Zheng and Z. Chen, “On properties of q-difference equations,” Acta Mathematica Scientia Series B, vol. 32, no. 2, pp. 724–734, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  17. L. Y. Gao, “On meromorphic solutions of a type of system of composite functional equations,” Acta Mathematica Scientia, vol. 32, no. 2, pp. 800–806, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  18. L. Y. Gao, “Systems of complex difference equations of Malmquist type,” Acta Mathematica Sinica. Chinese Series, vol. 55, no. 2, pp. 293–300, 2012. View at Google Scholar · View at MathSciNet
  19. L. Y. Gao, “Estimates of N-function and m-function of meromorphic solutions of systems of complex difference equations,” Acta Mathematica Scientia B, vol. 32, no. 4, pp. 1495–1502, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  20. H.-Y. Xu, B.-X. Liu, and K.-Z. Tang, “Some properties of meromorphic solutions of systems of complex q-shift difference equations,” Abstract and Applied Analysis, vol. 2013, Article ID 680956, 6 pages, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  21. H.-Y. Xu and Z.-X. Xuan, “Some properties of solutions of a class of systems of complex q-shift difference equations,” Advances in Difference Equations, vol. 2013, article 271, 2013. View at Publisher · View at Google Scholar · View at Scopus
  22. S. A. Gao, Z. X. Chen, and T. W. Chen, Complex Oscillation Theory of Linear Differential Equations, Huazhong University of Science and Technology Press, Wuhan, China, 1997.
  23. J. He and X. M. Zheng, “The iterated order of meromorphic solutions of some classes of higher order linear differential equations,” Journal of Jiangxi Normal University. Natural Sciences, vol. 36, no. 6, pp. 584–588, 2012. View at Google Scholar
  24. I. Laine, Nevanlinna Theory and Complex Differential Equations, Walter de Gruyter, Berlin, Germany, 1993. View at Publisher · View at Google Scholar · View at MathSciNet
  25. J. Tu, H. X. Huang, H. Y. Xu, and C. F. Chen, “The order and type of meromorphic functions and analytic functions in the unit disc,” Journal of Jiangxi Normal University. Natural Science, vol. 37, no. 5, pp. 449–452, 2013. View at Google Scholar
  26. L. W. Liao, “The new developments in the research of nonlinear complex differential equations,” Journal of Jiangxi Normal University. Natural Sciences, vol. 39, no. 4, pp. 331–339, 2015. View at Google Scholar
  27. K. Liu and X. J. Dong, “Some results related to complex differential-difference equations of certain types,” Bulletin of the Korean Mathematical Society, vol. 51, no. 5, pp. 1453–1467, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  28. W. Bergweiler, K. Ishizaki, and N. Yanagihara, “Meromorphic solutions of some functional equations,” Methods and Applications of Analysis, vol. 5, no. 3, pp. 248–259, 1998, Correction: Methods and Applications of Analysis, vol. 6, no. 4, pp. 617-618, 1999. View at Google Scholar
  29. R. Goldstein, “Some results on factorisation of meromorphic functions,” Journal of the London Mathematical Society, vol. 4, no. 2, pp. 357–364, 1971. View at Google Scholar · View at MathSciNet
  30. G. G. Gundersen, “Finite order solutions of second order linear differential equations,” Transactions of the American Mathematical Society, vol. 305, no. 1, pp. 415–429, 1988. View at Publisher · View at Google Scholar · View at MathSciNet
  31. R. Goldstein, “On meromorphic solutions of certain functional equations,” Aequationes Mathematicae, vol. 18, no. 1-2, pp. 112–157, 1978. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  32. G. Jank and L. Volkmann, Einführung in die Theorie der Ganzen und Meromorphen Funktionen mit Anwendungen auf Differentialgleichungen, Birkhäuser, Basel, Switzerland, 1985.