On non-normal solutions of linear differential equations

Gröhn, Janne

doi:10.1090/proc/13292

On non-normal solutions of linear differential equations
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Proc. Amer. Math. Soc. 145 (2017), 1209-1220 Request permission

Abstract:

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 a differential equation may admit a non-normal solution having prescribed uniformly separated zeros.

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