TY - JOUR
T1 - Entire Solutions of Certain Type of Non-Linear Difference Equations
AU - Chen, Min Feng
AU - Gao, Zong Sheng
AU - Zhang, Ji Long
N1 - Publisher Copyright:
© 2018, Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2019/3/8
Y1 - 2019/3/8
N2 - In this paper, we study the existence of entire solutions of finite-order of non-linear difference equations of the form fn(z)+q(z)Δcf(z)=p1eα1z+p2eα2z,n≥2and fn(z)+q(z)eQ(z)f(z+c)=p1eλz+p2e-λz,n≥3where q, Q are non-zero polynomials, c, λ, p i , α i (i= 1 , 2) are non-zero constants such that α 1 ≠ α 2 and Δ c f(z) = f(z+ c) - f(z) ≢ 0. Our results are improvements and complements of Wen et al. (Acta Math Sin 28:1295–1306, 2012), Yang and Laine (Proc Jpn Acad Ser A Math Sci 86:10–14, 2010) and Zinelâabidine (Mediterr J Math 14:1–16, 2017).
AB - In this paper, we study the existence of entire solutions of finite-order of non-linear difference equations of the form fn(z)+q(z)Δcf(z)=p1eα1z+p2eα2z,n≥2and fn(z)+q(z)eQ(z)f(z+c)=p1eλz+p2e-λz,n≥3where q, Q are non-zero polynomials, c, λ, p i , α i (i= 1 , 2) are non-zero constants such that α 1 ≠ α 2 and Δ c f(z) = f(z+ c) - f(z) ≢ 0. Our results are improvements and complements of Wen et al. (Acta Math Sin 28:1295–1306, 2012), Yang and Laine (Proc Jpn Acad Ser A Math Sci 86:10–14, 2010) and Zinelâabidine (Mediterr J Math 14:1–16, 2017).
KW - Entire solutions
KW - Exponential polynomial
KW - Nevanlinna theory
KW - Non-linear difference equations
UR - https://www.scopus.com/pages/publications/85062791446
U2 - 10.1007/s40315-018-0250-6
DO - 10.1007/s40315-018-0250-6
M3 - 文章
AN - SCOPUS:85062791446
SN - 1617-9447
VL - 19
SP - 17
EP - 36
JO - Computational Methods and Function Theory
JF - Computational Methods and Function Theory
IS - 1
ER -