Taiwanese Journal of Mathematics
- Taiwanese J. Math.
- Volume 15, Number 3 (2011), 1037-1057.
Meromorphic Solutions of Certain Functional Equations
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.
Taiwanese J. Math., Volume 15, Number 3 (2011), 1037-1057.
First available in Project Euclid: 18 July 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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