Taiwanese Journal of Mathematics

Meromorphic Solutions of Certain Functional Equations

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

https://projecteuclid.org/euclid.twjm/1500406283

Digital Object Identifier
doi:10.11650/twjm/1500406283

Mathematical Reviews number (MathSciNet)
MR2829896

Zentralblatt MATH identifier
1238.30022

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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