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Sbornik: Mathematics, 2015, Volume 206, Issue 12, Pages 1731–1770
DOI: https://doi.org/10.1070/SM2015v206n12ABEH004512 (Mi sm8417) 		 
This article is cited in 10 scientific papers (total in 10 papers)

Disconjugacy of fourth-order equations on graphs

R. Ch. Kulaevab

a Southern Mathematical Institute of the Vladikavkaz Scientific Center of the Russian Academy of Sciences
b North-Ossetia State University, Vladikavkaz
English version PDF (722 kB) Citations (10)
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DOI: https://doi.org/10.1070/SM2015v206n12ABEH004512
Abstract: This paper develops the theory of disconjugacy of fourth-order equations on geometric graphs which arises in modelling rod structures. The disconjugacy of an equation is defined in terms of a special fundamental system of solutions of the homogeneous equation. The disconjugacy property is shown to be related to the positivity property of the Green's functions for certain classes of boundary value problems for a fourth-order equation on a graph. A maximum principle for a fourth-order equation on a graph is formulated, and some properties of differential inequalities are proved.
Bibliography: 25 titles.
Keywords: disconjugacy, differential equation on a graph, Green's function, maximum principle, conjugacy.
Received: 25.08.2014 and 01.08.2015
Russian version:
Matematicheskii Sbornik, 2015, Volume 206, Number 12, Pages 79–118
DOI: https://doi.org/10.4213/sm8417
Bibliographic databases:
Document Type: Article
UDC: 517.927.6
MSC: 34B45
Language: English
Original paper language: Russian
Citation: R. Ch. Kulaev, “Disconjugacy of fourth-order equations on graphs”, Mat. Sb., 206:12 (2015), 79–118; Sb. Math., 206:12 (2015), 1731–1770
Citation in format AMSBIB
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  • https://doi.org/10.1070/SM2015v206n12ABEH004512
  • https://www.mathnet.ru/eng/sm/v206/i12/p79
    • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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    Abstract page:550
    Russian version PDF:175
    English version PDF:23
    References:44
    First page:35
     
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