Geodesic
On the Multiplicity of Eigenvalues of the Sturm--Liouville Problem on Graphs
Matematičeskie zametki, Tome 99 (2016) no. 4, pp. 489-501

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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.
Keywords: geometric graph, ordinary differential equation on a graph, multiplicity of eigenvalues.
Mots-clés : Sturm–Liouville problem on a graph, transmission conditions 
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     author = {A. T. Diab and B. K. Kaldybekova and O. M. Penkin},
     title = {On the {Multiplicity} of {Eigenvalues} of the {Sturm--Liouville} {Problem} on {Graphs}},
     journal = {Matemati\v{c}eskie zametki},
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     publisher = {mathdoc},
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     number = {4},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2016_99_4_a1/}
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A. T. Diab; B. K. Kaldybekova; O. M. Penkin. On the Multiplicity of Eigenvalues of the Sturm--Liouville Problem on Graphs. Matematičeskie zametki, Tome 99 (2016) no. 4, pp. 489-501. http://geodesic.mathdoc.fr/item/MZM_2016_99_4_a1/