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Zbl 0890.30019
Yang, Chung-Chun; Hua, Xinhou
Uniqueness and value-sharing of meromorphic functions.
(English)
[J] Ann. Acad. Sci. Fenn., Math. 22, No.2, 395-406 (1997). ISSN 1239-629X

Concerning the uniqueness and sharing values of meromorphic functions, many results about meromorphic functions that share more than or equal to two values have been obtained. In this paper, we study meromorphic functions that share only one value, and prove the following result: For $n\geq 11$ and two meromorphic functions $f(z)$ and $g(z)$, if $f^nf'$ and $g^ng'$ share the same nonzero and finite value $a$ with the same multiplicities, then $f\equiv dg$ or $g=c_1 e^{cz}$ and $f=c_2e^{-cz}$, where $d$ is an $(n+1)$th root of unity, $c$, $c_1$ and $c_2$ being constants. As applications, we solve some nonlinear differential equations.
[X.Hua (Nanjing)]
MSC 2000:
*30D35 Distribution of values (one complex variable)

Keywords: value-sharing; meromorphic functions; nonlinear differential equations

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