• Wang, Songmin (Department of Basic The Chinese People's Armed Police Forces Academy) ;
  • Li, Sheng (College of Science Guangdong Ocean University)
  • Received : 2011.09.21
  • Published : 2013.09.30


In this paper, we study the non-existence of finite order entire solutions of nonlinear differential-difference of the form $$f^n+Q(z,f)=h$$, where $n{\geq}2$ is an integer, $Q(z,f)$ is a differential-difference polynomial in $f$ with polynomial coefficients, and $h$ is a meromorphic function of order ${\leq}1$.


  1. 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), no. 1, 105-129.
  2. J. Clunie, On integral and meromorphic functions, J. London Math. Soc. 37 (1962), 17-27.
  3. R. G. Halburd and R. J. Korhonen, Difference analogue of the lemma on the logarithmic derivative with applications to difference equations, J. Math. Anal. Appl. 314 (2006), no. 2, 477-487.
  4. W. K. Hayman, Meromorphic Functions, Clarendon Press, Oxford, 1964.
  5. J. Heittokangas, R. Korhonen, and I. Laine, On meromorphic solutions of certain non-linear differential equations, Bull. Austral. Math. Soc. 66 (2002), no. 2, 331-343.
  6. I. Laine, Nevanlinna Theory and Complex Differential Equations, De Gruyter, Berlin, 1993.
  7. I. Laine and C. C. Yang, Clunie theorems for difference and q-difference polynomials, J. Lond. Math. Soc. (2) 76 (2007), no. 3, 556-566.
  8. P. Li and C. C. Yang, On the nonexistence of entire solutions of certain type of nonlinear differential equations, J. Math. Anal. Appl. 302 (2006), no. 2, 827-835.
  9. C. C. Yang and I. Laine, On analogies between nonlinear difference and differential equations, Proc. Japan Acad. Ser. A Math. Sci. 86 (2010), no. 1, 10-14.
  10. C. C. Yang and P. Li, On the transcendental solutions of a certain type of nonlinear differential equations, Arch. Math. (Basel) 82 (2004), no. 5, 442-448.
  11. C. C. Yang and Z. Ye, Estimates of the proximate function of differential polynomials, Proc. Japan Acad. Ser. A Math. Sci. 83 (2007), no. 4, 50-55.

Cited by

  1. Exponential Polynomials as Solutions of Differential-Difference Equations of Certain Types vol.13, pp.5, 2016,
  2. Meromorphic Solutions of Complex Differential–Difference Equations 2017,
  3. Good Linear Operators and Meromorphic Solutions of Functional Equations vol.2015, 2015,