  Normality arguments are applied to study the oscillation of solutions of
$f''+Af=0$, where the coefficient $A$ is analytic in the unit disc $\mathbb{D}$
and $\sup_{z\in\mathbb{D}} (1-|z|^2)^2|A(z)| < \infty$. It is shown that such
differential equation may admit a non-normal solution having prescribed
uniformly separated zeros.
