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Funktsional'nyi Analiz i ego Prilozheniya, 2013, Volume 47, Issue 4, Pages 18–29
DOI: https://doi.org/10.4213/faa3124 (Mi faa3124) 		 
This article is cited in 16 scientific papers (total in 16 papers)

On the Neumann Problem for the Sturm–Liouville Equation with Cantor-Type Self-Similar Weight

A. A. Vladimirova, I. A. Sheipakb

a Dorodnitsyn Computing Centre of the Russian Academy of Sciences, Moscow
b M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Full-text PDF (191 kB) Citations (16)
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DOI: https://doi.org/10.4213/faa3124
Abstract: The second and third boundary value problems for the Sturm–Liouville equation in which the weight function is the generalized derivative of a Cantor-type self-similar function are considered. The oscillation properties of the eigenfunctions of these problems are studied, and on the basis of this study, known asymptotics of their spectra are substantially refined. Namely, it is proved that the function $s$ in the well-known formula
$$ N(\lambda)=\lambda^D\cdot [s(\ln\lambda)+o(1)] $$
decomposes into the product of a decreasing exponential and a nondecreasing purely singular function (and, thereby, is not constant).
Keywords: Sturm–Liouville problem, self-similar weight, Neumann boundary conditions, third-type boundary conditions, spectral periodicity.
Received: 20.05.2011
English version:
Functional Analysis and Its Applications, 2013, Volume 47, Issue 4, Pages 261–270
DOI: https://doi.org/10.1007/s10688-013-0033-9
Bibliographic databases:
Document Type: Article
UDC: 517.984
Language: Russian
Citation: A. A. Vladimirov, I. A. Sheipak, “On the Neumann Problem for the Sturm–Liouville Equation with Cantor-Type Self-Similar Weight”, Funktsional. Anal. i Prilozhen., 47:4 (2013), 18–29; Funct. Anal. Appl., 47:4 (2013), 261–270
Citation in format AMSBIB
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    • This publication is cited in the following 16 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Функциональный анализ и его приложения Functional Analysis and Its Applications
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