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Mat. Sb., 2015, Volume 206, Number 12, Pages 79–118 (Mi msb8417)  

This article is cited in 1 scientific paper (total in 1 paper)

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

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.

DOI: https://doi.org/10.4213/sm8417

Full text: PDF file (767 kB)
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English version:
Sbornik: Mathematics, 2015, 206:12, 1731–1770

Bibliographic databases:

UDC: 517.927.6
MSC: 34B45
Received: 25.08.2014 and 01.08.2015

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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Linking options:
  • http://mi.mathnet.ru/eng/msb8417
  • https://doi.org/10.4213/sm8417
  • http://mi.mathnet.ru/eng/msb/v206/i12/p79

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. R. Ch. Kulaev, “K voprosu o neostsillyatsii differentsialnogo uravneniya na grafe”, Vladikavk. matem. zhurn., 19:3 (2017), 31–40  mathnet
  • Математический сборник Sbornik: Mathematics (from 1967)
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