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Sibirsk. Mat. Zh., 2016, Volume 57, Number 1, Pages 85–97 (Mi smj2730)  

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

On the disconjugacy property of an equation on a graph

R. Ch. Kulaevab

a Southern Mathematical Institute, Vladikavkaz Scientific Center of the Russian Academy of Sciences, Vladikavkaz, Russia
b Khetagurov North Ossetian State University, Vladikavkaz, Russia

Abstract: Under study is the disconjugacy theory of forth order equations on a geometric graph. The definition of disconjugacy is given in terms of a special fundamental system of solutions to a homogeneous equation. We establish some connections between the disconjugacy property and the positivity of the Green's functions for several classes of boundary value problems for forth order equation on a graph. We also state the maximum principle for a forth order equation on a graph and prove some properties of differential inequalities.

Keywords: graph, differential equation on a graph, disconjugacy, Green’s function, maximum principle, differential inequality.

DOI: https://doi.org/10.17377/smzh.2016.57.107

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English version:
Siberian Mathematical Journal, 2016, 57:1, 64–73

Bibliographic databases:

UDC: 517.955
Received: 11.04.2015

Citation: R. Ch. Kulaev, “On the disconjugacy property of an equation on a graph”, Sibirsk. Mat. Zh., 57:1 (2016), 85–97; Siberian Math. J., 57:1 (2016), 64–73

Citation in format AMSBIB
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\paper On the disconjugacy property of an equation on a~graph
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\jour Siberian Math. J.
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\pages 64--73
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    Citing articles on Google Scholar: Russian citations, English citations
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    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
  • Сибирский математический журнал Siberian Mathematical Journal
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