ON ENTIRE SOLUTIONS OF NONLINEAR DIFFERENCE-DIFFERENTIAL EQUATIONS

- Journal title : Bulletin of the Korean Mathematical Society
- Volume 50, Issue 5, 2013, pp.1471-1479
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/BKMS.2013.50.5.1471

Title & Authors

ON ENTIRE SOLUTIONS OF NONLINEAR DIFFERENCE-DIFFERENTIAL EQUATIONS

Wang, Songmin; Li, Sheng;

Wang, Songmin; Li, Sheng;

Abstract

In this paper, we study the non-existence of finite order entire solutions of nonlinear differential-difference of the form , where is an integer, is a differential-difference polynomial in with polynomial coefficients, and is a meromorphic function of order .

Keywords

difference-differential polynomial;differential polynomial;difference-differential equation;Nevanlinna theory;

Language

English

Cited by

1.

References

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.