Meromorphic Solutions for a Class of Differential Equations and Their Applications

摘要

In this note, we study the admissible meromorphic solutions for algebraic differential equation f(n)f' + Pn-1(f) = R(z)e((z)), where Pn-1(f) is a differential polynomial in f of degree n - 1 with small function coefficients, R is a non-vanishing small function of f, and alpha is an entire function. We show that this equation does not possess any meromorphic solution f(z) satisfying N(r, f) = S(r, f) unless Pn-1(f) 0. Using this result, we generalize a well-known result by Hayman.