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Oscillation of solutions of LDE's in domains conformally equivalent to unit disc (1905.09487v1)
Published 23 May 2019 in math.CA and math.CV
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.