On spectral asymptotics of the Neumann problem for the Sturm-Liouville   equation with self-similar generalized Cantor type weight
  Spectral asymptotics of the Neumann problem for the Sturm-Liouville equation with generalized derivative of a self-similar generalized Cantor type function as a weight are considered. The spectrum is shown to have a periodicity property for a wide class of Cantor type self-similar functions, and also the weaker "quasi-periodicity" condition is demonstrated under certain mixed boundary conditions. This allows for a more precise description of the main term of the asymptotics of the counting function of eigenvalues. Previous results by A. A. Vladimirov, I. A. Sheipak are generalized. 
Nikita V. Rastegaev
math.SP