This article is cited in 1 paper

Lower bounds for the leading eigenvalue of the Laplacian on a graph

S. A. Karkuzaev^a, R. Ch. Kulaev<sup>b

a</sup> North Ossetian State University after Kosta Levanovich Khetagurov, Vladikavkaz
^b Southern Mathematical Institute of the Vladikavkaz Scientific Center of the Russian Academy of Sciences, Vladikavkaz

Abstract: The purpose of this paper is to obtain lower bounds for the minimal eigenvalue of the Sturm–Liouville differential operator on a graph. In this way, an analog of the Picone identity for an equation on a network is established. As an application of such an identity, Sturm comparison theorems and properties of differential inequalities for a second-order operator on a graph are obtained.

Keywords: eigenvalue estimation, spectral problem on a graph, Sturm theorems, Picone identity.

UDC: 517.927

MSC: 34C10, 34B27, 34B24, 34L05

Received: 06.04.2024

DOI: 10.4213/mzm14338

 English version: Mathematical Notes, 2025, 117:2, 287–299

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