# Oscillation of solutions of LDE's in domains conformally equivalent to unit disc

## TL;DR

This paper investigates the oscillation behavior of solutions to linear differential equations in domains conformally equivalent to the unit disc, introducing a new conformal transformation method and exploring zero-free solutions.

## Contribution

It presents a novel conformal transformation approach for higher order linear differential equations and analyzes oscillation in various conformally equivalent domains.

## Key findings

- Oscillation criteria established for solutions in specific domains.
- New conformal transformation method for higher order equations.
- Results on existence of zero-free solution bases.

## Abstract

Oscillation of solutions of $f^{(k)} + a_{k-2} f^{(k-2)} + \dotsb + a_1 f' +a_0 f = 0$ is studied in domains conformally equivalent to the unit disc. The results are applied, for example, to Stolz angles, horodiscs, sectors and strips. The method relies on a new conformal transformation of higher order linear differential equations. Information on the existence of zero-free solution bases is also obtained.