Oscillation method in the spectral problem for a fourth order differential operator with a self-similar weight

Vladimirov, A.

doi:10.1090/spmj/1385

Oscillation method in the spectral problem for a fourth order differential operator with a self-similar weight
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by A. A. Vladimirov
Translated by: A. Plotkin

St. Petersburg Math. J. 27 (2016), 237-244

DOI: https://doi.org/10.1090/spmj/1385

Published electronically: January 29, 2016

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Abstract:

Selfadjoint boundary problems are considered for the differential equation $y^{(4)}-\lambda \rho y=0$, where the weight $\rho \in W_2^{-1}[0,1]$ is the generalized derivative of a self-similar function of the Kantor type. On the basis of the study of oscillation properties of eigenfunctions, the characteristics of the known spectral asymptotics of such problems are refined.

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