Abstract
Bounds for the multiplicity of the eigenvalues of the Sturm–Liouville problem on a graph, which are valid for a wide class of consistency (transmission) conditions at the vertices of the graph, are given. The multiplicities are estimated using the topological characteristics of the graph. In the framework of the notions that we use, the bounds turn out to be exact.
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Original Russian Text © A. T. Diab, B. K. Kaldybekova, O. M. Penkin, 2016, published in Matematicheskie Zametki, 2016, Vol. 99, No. 4, pp. 489–501.
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Diab, A.T., Kaldybekova, B.K. & Penkin, O.M. On the multiplicity of eigenvalues of the Sturm–Liouville problem on graphs. Math Notes 99, 492–502 (2016). https://doi.org/10.1134/S0001434616030226
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DOI: https://doi.org/10.1134/S0001434616030226