On non-normal solutions of linear differential equations

Abstract

Normality arguments are applied to study the oscillation of solutions of $f^{\prime \prime }+Af=0$, 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.

arXiv comment11 pages