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This article is cited in 12 scientific papers (total in 12 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
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
Citation:
R. Ch. Kulaev, “Disconjugacy of fourth-order equations on graphs”, Sb. Math., 206:12 (2015), 1731–1770
Linking options:
https://www.mathnet.ru/eng/sm8417https://doi.org/10.1070/SM2015v206n12ABEH004512 https://www.mathnet.ru/eng/sm/v206/i12/p79
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Abstract page: | 564 | Russian version PDF: | 178 | English version PDF: | 25 | References: | 46 | First page: | 35 |
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