Non-linear differential equations and Hayman’s theorem on differential polynomials
Non-linear differential equations and Hayman’s theorem on differential polynomials
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非线性微分方程和微分多项式的海曼定理
DOI：
10.1080/17476933.2014.972390
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发表时间：
2015-06
影响因子：
0.9
通讯作者：
Liao L.-W.
中科院分区：
文献类型：
--
作者：
Liao L.-W.
In this paper, we first prove that if the following differential equationadmits a meromorphic function with finitely many poles, where and is a differential polynomial in with degree and rational functions as its coefficients, is a non-zero rational function and is a non-constant polynomial, then has the form and where is a rational function and is a polynomial with With this in hand, we prove if is a transcendental entire function, is a polynomial of degree , then assumes every complex number infinitely many times, except a possible value . On the other hand, if assumes the complex value finitely many times, then and .
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DOI：
10.1515/9783110863147
发表时间：
1992-12
期刊：
--
影响因子：
--
作者：
I. Laine
通讯作者：
I. Laine
DOI：
10.1090/s0002-9947-1968-0220936-0
发表时间：
1968
影响因子：
1.3
作者：
F. Gross
通讯作者：
F. Gross
影响因子：
1.3
作者：
L. Zalcman
通讯作者：
L. Zalcman
影响因子：
2.2
作者：
Chung-Chun Yang
通讯作者：
Chung-Chun Yang
影响因子：
4.1
作者：
T. Shimizu;K. Yosida;S. Kakutani
通讯作者：
T. Shimizu;K. Yosida;S. Kakutani