科研之友
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摘要
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 p function.
- 出版日期2011-6
- 单位中国科学技术大学
