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

Abstract

Oscillation of solutions of $f^{(k)}+a_{k-2}{f}^{(k-2)}+\cdots +a_1{f}^{\prime }+a_{0}f=0$ 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.

14 pages