[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/BKMS.b160844

ON SOME SPECIAL DIFFERENCE EQUATIONS OF MALMQUIST TYPE

Zhang, Jie (School of Mathematics China University of Mining and Technology)

Publication Information

Bulletin of the Korean Mathematical Society / v.55, no.1, 2018 , pp. 51-61 More about this Journal

Abstract

In this article, we mainly use Nevanlinna theory to investigate some special difference equations of malmquist type such as $f^2+({\Delta}_cf)^2={\beta}^2$ , $f^2+({\Delta}_cf)^2=R$ , $f{^{\prime}^2}+({\Delta}_cf)^2=R$ and $f^2+(f(z+c))^2=R$ , where ${\beta}$ is a nonzero small function of f and R is a nonzero rational function respectively. These discussions extend one related result due to C. C. Yang et al. in some sense

Keywords

Nevanlinna theory; uniqueness; difference equation; differential equation;

Citations & Related Records

Times Cited By KSCI : 1 (Citation Analysis)

Reference
Cited By KSCI

1	Y. M. Chiang and S. J. Feng, On the growth of logarithmic differences, difference quotients and logarithmic derivatives of meromorphic functions, Trans. Amer. Math. Soc. 361 (2009), no. 7, 3767-3791. DOI
2	W. K. Hayman, Meromorphic Functions, Clarendon Press, Oxford, 1964.
3	I. Laine and C. C. Yang, Clunie theorem for difference and q-difference polynomials, J. London Math. Soc. 76 (2007), no. 3, 556-566. DOI
4	K. Liu and L. Z. Yang, On entire solutions of some differential-difference equations, Comput. Methods Funct. Theory. 13 (2013), no. 3, 433-447. DOI
5	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. DOI
6	C. C. Yang and H. X. Yi, Uniqueness theory of meromorphic functions, Science Press, Beijing, Second Printed in 2006.
7	L. Yang, Value Distribution Theory, Springer-Verlag & Science Press, Berlin, 1993.
8	J. Zhang, Existence of entire solution of some certain type difference equation, Houston J. Math. 39 (2013), no. 2, 625-635.
9	Y. M. Chiang and S. J. Feng, On the Nevanlinna characteristic of $f(z+{\eta})$ and difference equations in the complex plane, Ramanujian J. 16 (2008), no. 1, 105-129. DOI
10	W. Chen, P. C. Hu, and Y. Y. Zhang, On solutions to some nonlinear difference and differential equations, J. Korean Math. Soc. 53 (2016), no. 4, 835-846. DOI