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.
Citation
Mingbo Yang. Ping Li. "Meromorphic Solutions of Certain Functional Equations." Taiwanese J. Math. 15 (3) 1037 - 1057, 2011. https://doi.org/10.11650/twjm/1500406283
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