Normal families of meromorphic functions with multiple poles

Abstract

Let $\mathcal{F}$ be a family of meromorphic functions defined in a domain $\mathcal{D}$, and $a,\ b$ be two constants such that $a\neq 0,\ \infty$ and $b\neq \infty$. If for each $f\in \mathcal{F}$, all poles of $f(z)$ are of multiplicity at least $3$ in $\mathcal{D}$, and $f'(z)+af^2(z)-b$ has at most 1 zero in $\mathcal{D}$, ignoring multiplicity, then $\mathcal{F}$ is normal in $\mathcal{D}$.