# Description of growth and oscillation of solutions of complex LDE's

@article{Chyzhykov2019DescriptionOG, title={Description of growth and oscillation of solutions of complex LDE's}, author={Igor Chyzhykov and Janne Grohn and Janne Heittokangas and Jouni Rattya}, journal={arXiv: Classical Analysis and ODEs}, year={2019} }

It is known that, equally well in the unit disc as in the whole complex plane, the growth of the analytic coefficients $A_0,\dotsc,A_{k-2}$ of \begin{equation*} f^{(k)} + A_{k-2} f^{(k-2)} + \dotsb + A_1 f'+ A_0 f = 0, \quad k\geq 2, \end{equation*} determines, under certain growth restrictions, not only the growth but also the oscillation of its non-trivial solutions, and vice versa. A uniform treatment of this principle is given in the disc $D(0,R)$, $0<R\leq \infty$, by using several…

## 4 Citations

Irregular finite order solutions of complex LDE's in unit disc

- Mathematics
- 2020

It is shown that the order and the lower order of growth are equal for all non-trivial solutions of $f^{(k)}+A f=0$ if and only if the coefficient $A$ is analytic in the unit disc and $\log^+…

On the number of linearly independent admissible solutions to linear differential and linear difference equations

- MathematicsCanadian Journal of Mathematics
- 2020

Abstract A classical theorem of Frei states that if
$A_p$
is the last transcendental function in the sequence
$A_0,\ldots ,A_{n-1}$
of entire functions, then each solution base of the…

Logarithmic derivative estimates of meromorphic functions of finite order in the half-plane

- 2020

I. E. Chyzhykov, A. Z. Mokhon’ko. Logarithmic derivative estimates of meromorphic functions of finite order in the half-plane, Mat. Stud. 54 (2020), 172–187. We established new sharp estimates…

Oscillation of Solutions of LDE’s in Domains Conformally Equivalent to Unit Disc

- MathematicsThe Journal of Geometric Analysis
- 2022

<jats:p>Oscillation of solutions of <jats:inline-formula><jats:alternatives><jats:tex-math>$$f^{(k)} + a_{k-2} f^{(k-2)} + \cdots + a_1 f' +a_0 f = 0$$</jats:tex-math><mml:math…

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