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Necessary and sufficient condition for the positivity of the Green function of a boundary value problem for a fourth-order equation on a graph

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Abstract

We study the sign properties of the Green function of a boundary value problem for a fourth-order equation on a graph. We obtain necessary and sufficient conditions for the positivity of the Green function. The conditions are stated in terms of the properties of a uniquely determined system of solutions of the equation on the graph, which permits one to verify them by computer methods.

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Authors and Affiliations

  1. South Mathematical Institute, Vladikavkaz Scientific Center, Russian Academy of Sciences, Vladikavkaz, Russia

    R. Ch. Kulaev

  2. 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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Original Russian Text © R.Ch. Kulaev, 2015, published in Differentsial’nye Uravneniya, 2015, Vol. 51, No. 3, pp. 302–316.

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Kulaev, R.C. Necessary and sufficient condition for the positivity of the Green function of a boundary value problem for a fourth-order equation on a graph. Diff Equat 51, 303–317 (2015). https://doi.org/10.1134/S0012266115030039

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  • DOI: https://doi.org/10.1134/S0012266115030039

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