Acta mathematica scientia, Series B >
ON GROWTH OF MEROMORPHIC SOLUTIONS OF NONLINEAR DIFFERENCE EQUATIONS AND TWO CONJECTURES OF C.C.YANG
Received date: 2014-10-27
Revised date: 2015-03-09
Online published: 2016-01-30
Supported by
The first author is supported by the NNSF of China(11171013, 11371225, 11201014), the YWF-14-SXXY-008 of Beihang University, and the Fundamental Research Funds for the Central University.
In this paper, we investigate the growth of the meromorphic solutions of the following nonlinear difference equations f(z)n+Pn-1(f)=0, where n≥2 and Pn-1(f) is a difference polynomial of degree at most n-1 in f with small functions as coefficients.Moreover, we give two examples to show that one conjecture proposed by Yang and Laine [2] does not hold in general if the hyper-order of f(z) is no less than 1.
Key words： growth; meromorphic solutions; difference equations; conjectures
Yueyang ZHANG , Zongsheng GAO , Jilong ZHANG . ON GROWTH OF MEROMORPHIC SOLUTIONS OF NONLINEAR DIFFERENCE EQUATIONS AND TWO CONJECTURES OF C.C.YANG[J]. Acta mathematica scientia, Series B, 2016 , 36(1) : 195 -202 . DOI: 0.1016/S0252-9602(15)30087-4
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