Taiwanese Journal of Mathematics

Meromorphic Solutions of Certain Functional Equations

Mingbo Yang and Ping Li

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Abstract

By utilizing Nevanlinna's value distribution theory, we study the existence or solvability of meromorphic solutions of functional equations of the type $P(f) f'P(g) g' = 1$, where $P(z)$ is a polynomial with two distinct zeros at least. We show that such type of equations have no meromorphic solutions $f$ and $g$ when $P(z)$ has at least three distinct zeros. Moreover, for some polynomials $P(z)$ with two distinct zeros only, such type of equations possess transcendental meromorphic solutions which can be expressed by Weierstrass $\wp$ function.

Article information

Source
Taiwanese J. Math., Volume 15, Number 3 (2011), 1037-1057.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500406283

Digital Object Identifier
doi:10.11650/twjm/1500406283

Mathematical Reviews number (MathSciNet)
MR2829896

Zentralblatt MATH identifier
1238.30022

Subjects
Primary: 30D35: Distribution of values, Nevanlinna theory 30D05: Functional equations in the complex domain, iteration and composition of analytic functions [See also 34Mxx, 37Fxx, 39-XX]

Keywords
meromorphic function functional equation uniqueness

Citation

Yang, Mingbo; Li, Ping. Meromorphic Solutions of Certain Functional Equations. Taiwanese J. Math. 15 (2011), no. 3, 1037--1057. doi:10.11650/twjm/1500406283. https://projecteuclid.org/euclid.twjm/1500406283


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