TY - JOUR
T1 - On growth of meromorphic solutions of nonlinear difference equations and two conjectures of C.C. Yang
AU - Zhang, Yueyang
AU - Gao, Zongsheng
AU - Zhang, Jilong
N1 - Publisher Copyright:
© 2016 Wuhan Institute of Physics and Mathematics.
PY - 2016/1/1
Y1 - 2016/1/1
N2 - In this paper, we investigate the growth of the meromorphic solutions of the following nonlinear difference equationsf(z)n+P n-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.
AB - In this paper, we investigate the growth of the meromorphic solutions of the following nonlinear difference equationsf(z)n+P n-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.
KW - Conjectures
KW - Difference equations
KW - Growth
KW - Meromorphic solutions
UR - https://www.scopus.com/pages/publications/84949664169
U2 - 10.1016/S0252-9602(15)30087-4
DO - 10.1016/S0252-9602(15)30087-4
M3 - 文章
AN - SCOPUS:84949664169
SN - 0252-9602
VL - 36
SP - 195
EP - 202
JO - Acta Mathematica Scientia
JF - Acta Mathematica Scientia
IS - 1
ER -