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On the disconjugacy property of an equation on a graph

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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.

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Authors and Affiliations

  1. Southern Mathematical Institute, Vladikavkaz, Russia

    R. Ch. Kulaev

  2. Khetagurov North Ossetian State University, Vladikavkaz, Russia

    R. Ch. Kulaev

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  1. R. Ch. Kulaev
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Correspondence to R. Ch. Kulaev.

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Vladikavkaz. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 57, No. 1, pp. 85–97, January–February, 2016; DOI: 10.17377/smzh.2016.57.107.

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Kulaev, R.C. On the disconjugacy property of an equation on a graph. Sib Math J 57, 64–73 (2016). https://doi.org/10.1134/S0037446616010079

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  • DOI: https://doi.org/10.1134/S0037446616010079

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