Meromorphic Solutions for a Class of Differential Equations and Their Applications

被引：0
|
作者：
W. R. Lü
F. Lü
L. Wu
J. Yang
机构：
[1] China University of Petroleum,
来源：
Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences) | 2018年 / 53卷
关键词：
Differential polynomial; admissible solution; Hayman’s alternative; differential equation; small function; 30D35; 30D20; 30D30;
D O I：
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学科分类号：
摘要：
In this note, we study the admissible meromorphic solutions for algebraic differential equation fnf' + Pn−1(f) = R(z)eα(z), where Pn−1(f) is a differential polynomial in f of degree ≤ n − 1 with small function coefficients, R is a non-vanishing small function of f, and α is an entire function. We show that this equation does not possess any meromorphic solution f(z) satisfying N(r, f) = S(r, f) unless Pn−1(f) ≡ 0. Using this result, we generalize a well-known result by Hayman.
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页码：260 / 265
页数：5
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