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Vladikavkaz. Mat. Zh., 2017, Volume 19, Number 3, Pages 31–40 (Mi vmj622)  

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

On the disconjugacy of a differential equation on a graph

R. Ch. Kulaevab

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

Abstract: The paper is devoted to the problems of disconjugacy of fourth-order differential equations on a graph. We introduce the concept of critical disconjugacy. Critical disconjugacy allows us to generalize the notion of exact interval of disconjugacy in the classical theory. We give the definition of disconjugacy in terms of the properties of a special fundamental system of solutions of an equation on a graph. This definition introduces new features into the theory, but it preserves the basic properties of the one-dimensional theory.

Key words: differential equation on a graph, disconjugacy, boundary value problem, Green's function.

Full text: PDF file (236 kB)
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UDC: 517.955
Received: 10.07.2017

Citation: R. Ch. Kulaev, “On the disconjugacy of a differential equation on a graph”, Vladikavkaz. Mat. Zh., 19:3 (2017), 31–40

Citation in format AMSBIB
\Bibitem{Kul17}
\by R.~Ch.~Kulaev
\paper On the disconjugacy of a differential equation on a graph
\jour Vladikavkaz. Mat. Zh.
\yr 2017
\vol 19
\issue 3
\pages 31--40
\mathnet{http://mi.mathnet.ru/vmj622}


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    This publication is cited in the following articles:
    1. A. A. Vladimirov, E. S. Karulina, “Oscillation Properties of a Multipoint Fourth-Order Boundary-Value Problem with Spectral Parameter in the Boundary Condition”, Math. Notes, 106:6 (2019), 899–903  mathnet  crossref  crossref  isi
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