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.
Categories: math.CA math.CV