Meromorphic Solutions of Generalized Algebraic Differential Equations

摘要

The rate of growth of meromorphic functions f, which are solutions of algebraic differential equations whose coefficients a(z) are arbitrary meromorphic functions, is investigated. By a method based on Nevanlinna's theory of meromorphic functions, it has been shown that if f'/f has infinity as its Nevanlinna exceptional values, then the ratio T(r, f'/f)/T(r, a(z)), as r approaches infinity outside a set of r values of finite measure, is bounded for at least one of the coefficients a(z). (Author)