Geodesic
On spectral asymptotics of the Neumann problem for the Sturm--Liouville equation with self-similar generalized Cantor type weight
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 44, Tome 425 (2014), pp. 86-98

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Spectral asymptotics of the weighted Neumann problem for the Sturm–Liouville equation is considered. The weight is assumed to be the distributional derivative of a self-similar generalized Cantor type function. The spectrum is shown to have a periodicity property for a wide class of Cantor type self-similar functions. The weaker “quasi-periodicity” property is demonstrated under certain mixed boundary value conditions. This allows for a more precise description of the main term of the eigenvalue counting function asymptotics. Previous results by A. A. Vladimirov and I. A. Sheipak are generalized. 
@article{ZNSL_2014_425_a5,
     author = {N. V. Rastegaev},
     title = {On spectral asymptotics of the {Neumann} problem for the {Sturm--Liouville} equation with self-similar generalized {Cantor} type weight},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {86--98},
     publisher = {mathdoc},
     volume = {425},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2014_425_a5/}
}
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N. V. Rastegaev. On spectral asymptotics of the Neumann problem for the Sturm--Liouville equation with self-similar generalized Cantor type weight. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 44, Tome 425 (2014), pp. 86-98. http://geodesic.mathdoc.fr/item/ZNSL_2014_425_a5/