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Funktsional'nyi Analiz i ego Prilozheniya, 2005, Volume 39, Issue 2, Pages 78–81
DOI: https://doi.org/10.4213/faa44 (Mi faa44) 		 
This article is cited in 28 scientific papers (total in 28 papers)

Brief communications

Ambarzumian's Theorem for a Sturm–Liouville Boundary Value Problem on a Star-Shaped Graph

V. N. Pyvovarchyk

Odessa State Academy of Building and Architecture
Full-text PDF (167 kB) Citations (28)
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DOI: https://doi.org/10.4213/faa44
Abstract: Ambarzumian's theorem describes the exceptional case in which the spectrum of a single Sturm–Liouville problem on a finite interval uniquely determines the potential. In this paper, an analog of Ambarzumian's theorem is proved for the case of a Sturm–Liouville problem on a compact star-shaped graph. This case is also exceptional and corresponds to the Neumann boundary conditions at the pendant vertices and zero potentials on the edges.
Keywords: inverse problem, Neumann boundary conditions, normal eigenvalue, multiplicity of an eigenvalue, least eigenvalue, minimax principle.
Received: 24.07.2003
English version:
Functional Analysis and Its Applications, 2005, Volume 39, Issue 2, Pages 148–151
DOI: https://doi.org/10.1007/s10688-005-0029-1
Bibliographic databases:
Document Type: Article
UDC: 517.5+517.43
Language: Russian
Citation: V. N. Pyvovarchyk, “Ambarzumian's Theorem for a Sturm–Liouville Boundary Value Problem on a Star-Shaped Graph”, Funktsional. Anal. i Prilozhen., 39:2 (2005), 78–81; Funct. Anal. Appl., 39:2 (2005), 148–151
Citation in format AMSBIB
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    • This publication is cited in the following 28 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Функциональный анализ и его приложения Functional Analysis and Its Applications
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