Meromorphic solutions of certain type of differential-difference equations

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:470

Article

Dong, Xianjing¹  Liao, Liangwen¹ 

[1] Nanjing Univ, Dept Math, Nanjing, Jiangsu, Peoples R China

关键词: Differential-difference equations;    Nevanlinna theory;    Order;    Meromorphic solutions;   

DOI  :  10.1016/j.jmaa.2018.10.005

来源: Elsevier

【 摘 要 】

We consider meromorphic solutions to general differential-difference equation of type L(z, f) + Sigma(q)(j = 1)c(j)(z)f(nj) (z + zeta(j)) = Sigma(r)(j = 1) gamma(j)e(lambda jz), where L(z, f) not equivalent to 0 is a linear differential-difference polynomial of f with small function coefficients, and 1 < n(1) < . . . < n(q), gamma(j)(1 <= j <= r) are nonvanishing constants, c(j)(z)(1 <= j <= q) are nonvanishing small functions. If the equation admits a transcendental meromorphic solution f of finite order satisfying that lambda(f) < sigma(f), lambda(1/f) < sigma(f), then representation of f and relations between coefficients in psi(z, f) and gamma(i,) lambda(j) can be obtained. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free