# On non-normal solutions of linear differential equations

@inproceedings{Grohn2016OnNS, title={On non-normal solutions of linear differential equations}, author={Janne Grohn}, year={2016} }

Normality arguments are applied to study the oscillation of solutions of f ′′ +Af = 0, where the coefficient A is analytic in the unit disc D and supz∈D(1 − |z| )|A(z)| < ∞. It is shown that such differential equation may admit a non-normal solution having prescribed uniformly separated zeros.

## 6 Citations

### On the Construction of Solutions of Linear Differential Equations According to Given Sequences

- MathematicsUkrainian Mathematical Journal
- 2018

We consider the problem under what conditions the equation f″ + Af = 0 possesses an entire (meromorphic) solution with given sequences of zeros (poles) and critical points. The results are extended…

### Solutions of complex differential equation having zeros on pre-given sequences

- Mathematics
- 2017

Behavior of solutions of f ′′ +Af = 0 is discussed under the assumption that A is analytic in D and sup z∈D (1 − |z|)|A(z)| < ∞, where D is the unit disc of the complex plane. As a main result it is…

### Growth estimates for meromorphic solutions of higher order algebraic differential equations

- MathematicsTohoku Mathematical Journal
- 2020

We establish pointwise growth estimates for the spherical derivative of solutions of the first order algebraic differential equations. A generalization of this result to higher order equations is…

### Solutions of Complex Differential Equation Having Pre-given Zeros in the Unit Disc

- Materials ScienceConstructive Approximation
- 2017

Behavior of solutions of f′′+Af=0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs}…

### Converse growth estimates for ODEs with slowly growing solutions

- Materials ScienceMathematische Zeitschrift
- 2020

Let f1,f2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek}…

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