Deficient and Ramified Small Functions for Admissible Solutions of Some Differential Equations II

Abstract

Let $\alpha_{j}(z)$, $j=1,2$, $a_{i}(z)$, $i=1,2,\ldots,6$ be meromorphic functions. Suppose the differential equation (*) $w'^3+\alpha_2(z)w'^2+\alpha_1(z)w'=a_6(z)w^6+\cdots+a_1(z)w+a_0(z)$ possesses an admissible solution $w(z)$. If $\eta(z)$ is a solution of (*) and small with respect to $w(z)$ and if (*) is irreducible, then $\eta(z)$ is a deficient or a ramified function for $w(z)$.