tailieunhanh - Báo cáo hóa học: " Some results about a special nonlinear difference equation and uniqueness of difference polynomial"

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: Some results about a special nonlinear difference equation and uniqueness of difference polynomial | Qi et al. Journal of Inequalities and Applications 2011 2011 50 http content 2011 1 50 3 Journal of Inequalities and Applications a SpringerOpen Journal RESEARCH Open Access Some results about a special nonlinear difference equation and uniqueness of difference polynomial Jianming Qi 1 Jie Ding2 and Taiying Zhu2 Correspondence qijianmingdaxia@ department of Mathematics and Physics Shanghai Dianji University Shanghai 200240 PR China Full list of author information is available at the end of the article Springer Abstract In this paper we continue to study a special nonlinear difference equation solutions of finite order entire function. We also continue to investigate the value distribution and uniqueness of difference polynomials of meromorphic functions. Our results which improve the results of Yang and Laine Proc. Jpn. Acad. Ser. A Math. Sci. 83 50-55 2007 Qi et al. Comput. Math. Appl. 60 1739-1746 2010 . Mathematics Subject Classification 2000 30D35 39B32 34M05. Keywords Meromorphic functions Nevanlinna Theory difference equation difference polynomial 1 Introduction Let f z be a meromorphic function in the whole complex plane c. It is assumed that the reader is familiar with the standard symbols and fundamental results of Nevanlinna theory such as the characteristic function T r f proximity function m r f counting function N r f the first and second main theorem etc. see 1 2 . The notation S r f denotes any quantity that satisfies the condition S r f o T r f as r possibly outside an exceptional set of r of finite linear measure. A meromorphic a z is called a small function off z if and only if T r a z S r f . A polynomial Q z f is called a differential-difference polynomial inf wheneverf is a polynomial inf z its derivatives and its shifts f z c with small functions off again as the coefficients. Denote Ac f f z c - f z and A f Aj1-1 Acf for all n e N n 2 where c is nonzero complex constant. Recently Yang and .