Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Meromorphic Solutions of Some Complex Difference Equations | Hindawi Publishing Corporation Advances in Difference Equations Volume 2009 Article ID 982681 10 pages doi 2009 982681 Research Article Meromorphic Solutions of Some Complex Difference Equations Zhi-Bo Huang and Zong-Xuan Chen School of Mathematical Sciences South China Normal University Guangzhou 510631 China Correspondence should be addressed to Zong-Xuan Chen chzx@ Received 27 January 2009 Accepted 28 May 2009 Recommended by Binggen Zhang The main purpose of this paper is to present the properties of the meromorphic solutions of complex difference equations of the form 2 J aj z njEjf z Cj R z f z where J is a collection of all subsets of 1 2 . n Cj j e J are distinct nonzero complex numbers f z is a transcendental meromorphic function aj z s are small functions relative to f z and R z f z is a rational function in f z with coefficients which are small functions relative to f z . Copyright 2009 . Huang and . Chen. 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. 1. Introduction We assume that the readers are familiar with the basic notations of Nevanlinna s value distribution theory see 1-3 . Recent interest in the problem of integrability of difference equations is a consequence of the enormous activity on Painleve differential equations and their discrete counterparts during the last decades. Many people study this topic and obtain some results see 4-15 . In 4 Ablowitz et al. obtained a typical result as follows. Theorem A. If a complex difference equation ao z a1 z f z ap ffif zff f z 1 f z - 1 - R z f zN Í Ar q bc z b1 z f z bq z f zf1 with rational coefficients Oi z i 0 1 . p and bj z j 0 1 . q admits a transcendental meromorphic solution of finite order then degfR z f z 2. 2 Advances in Difference Equations In 10 Heittokangas et al. extended and improved the above .
