On non-normal solutions of linear differential equations

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