On the multiplicity of eigenvalues of the Sturm–Liouville problem on graphs

A. T. Diab; B. K. Kaldybekova; O. M. Penkin

doi:10.1134/S0001434616030226

On the multiplicity of eigenvalues of the Sturm–Liouville problem on graphs

Authors: Diab A.T.¹, Kaldybekova B.K.², Penkin O.M.²^,3
Affiliations:
1. Ain Shams University
2. Kazakh–British Technical University
3. Voronezh State University
Issue: Vol 99, No 3-4 (2016)
Pages: 492-502
Section: Article
URL: https://journals.rcsi.science/0001-4346/article/view/149268
DOI: https://doi.org/10.1134/S0001434616030226
ID: 149268

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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.