Project Euclid

References

• M. Ablowitz, R. G. Halburd and Herbst, On the extension of Painlev\ptmrs é property to difference equations, Nonlinearty, 13 (2000), 889-905.
  Mathematical Reviews (MathSciNet): MR1759006
  Digital Object Identifier: doi:10.1088/0951-7715/13/3/321
  
• S. B. Bank and R. P. Kaufman, An extension of Hölder's theoremconcerning the Gamma function, Funkcial. Ekvac., 19 (1976), 53-63.
• Z. X. Chen, On growth, zeros and poles of meromorphic functions of linear and nonlinear difference equations, Sci. China, Ser. A, 54 (2011), 2123-2133.
  Mathematical Reviews (MathSciNet): MR2838125
  Zentralblatt MATH: 1238.30019
  Digital Object Identifier: doi:10.1007/s11425-011-4265-y
  
• Z. X. Chen and K. H. Shon, Some results on Riccati equations, Acta Mathematica Sinica, 27 (2011), 1091-1100.
  Zentralblatt MATH: 1218.30076
  Digital Object Identifier: doi:10.1007/s10114-011-9175-y
  
• Z. X. Chen and K. H. Shon, On zeros and fixed points of difference of meromorphic functions, J. Math. Anal. Appl., 344 (2008), 373-383.
  Mathematical Reviews (MathSciNet): MR2416313
  Zentralblatt MATH: 1144.30012
  Digital Object Identifier: doi:10.1016/j.jmaa.2008.02.048
  
• Z. X. Chen, Z. Huang and R. Zhang, On difference equations relationg to Gamma function, Acta Mathematica Sinica, 31 (2011), 1281-1294.
  Zentralblatt MATH: 1249.30100
  
• 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), 105-129.
  Zentralblatt MATH: 1152.30024
  Digital Object Identifier: doi:10.1007/s11139-007-9101-1
  
• R. G. Halburd and R. Korhonen, Difference analogue of the lemma on the logarithmic derivative with applications to difference equations, J. Math. Anal. Appl., 314 (2006), 477-487.
  Zentralblatt MATH: 1085.30026
  Digital Object Identifier: doi:10.1016/j.jmaa.2005.04.010
  
• R. G. Halburd and R. Korhonen, Existence of finite-order meromorphic solutions as a detector of integrability in difference equations, Physica D., 218 (2006), 191-203.
  Zentralblatt MATH: 1105.39019
  Digital Object Identifier: doi:10.1016/j.physd.2006.05.005
  
• R. G. Halburd and R. Korhonen, Finite-order meromorphic solutions and the discrete Painlev$\acute{e}$ equations, Proc. London Math. Soc., 94 (2007), 443-474.
  Zentralblatt MATH: 1119.39014
  
• W. K. Hayman, Meromorphic Functions, Clarendon Press, Oxford, 1964.
• E. Hille, Ordinary Differential Equations in the Complex Domain, Dover Publications, Inc., Mineola, NY, 1997.
  Zentralblatt MATH: 0901.34001
  
• K. Ishizaki, On difference Riccati equations and second order linear difference equations, Aequat. Math., 81 (2011), 185-198.
  Zentralblatt MATH: 1215.39021
  Digital Object Identifier: doi:10.1007/s00010-010-0060-z
  
• T. Kimura, On the iteration of analytic functions, Funkcial. Ekvac., 14 (1971), 197-238.
  Zentralblatt MATH: 0237.30008
  
• I. Laine, Nevanlinna Theory and Complex Differential Equations, Walter de Gruyter, Berlin, 1993.
  Zentralblatt MATH: 0784.30002
  
• I. Laine and C. C. Yang, Clunie theorems for difference and $q$-difference polymials, J. Lond. Math. Soc., 76 (2007), 556-566.
  Mathematical Reviews (MathSciNet): MR2377111
  Zentralblatt MATH: 1132.30013
  Digital Object Identifier: doi:10.1112/jlms/jdm073
  
• S. Shimomura, Entire solutions of a polynomial difference equation, J. Fac. Sci. Univ. Tokyo Sect. IA Math., 28 (1981), 253-266.
  Mathematical Reviews (MathSciNet): MR632999
  Zentralblatt MATH: 0469.30021
  
• N. Yanagihara, Meromorphic solutions of some difference equations, Funkcial. Ekvac., 23 (1980), 309-326.
  Zentralblatt MATH: 0474.30024