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Spectral asymptotics of the Neumann problem for the Sturm-Liouville equationwith generalized derivative of a self-similar generalized Cantor type functionas a weight are considered. The spectrum is shown to have a periodicityproperty for a wide class of Cantor type self-similar functions, and also theweaker "quasi-periodicity" condition is demonstrated under certain mixedboundary conditions. This allows for a more precise description of the mainterm of the asymptotics of the counting function of eigenvalues. Previousresults by A. A. Vladimirov, I. A. Sheipak are generalized.

On spectral asymptotics of the Neumann problem for the Sturm-Liouville equation with self-similar generalized Cantor type weight