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Abstract <p> 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. </p>

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Lower Bounds for the Leading Eigenvalue of the Laplacian on a Graph

  • 期刊论文

  • 发表日期：

    2025年2月1日

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  • S. A. Karkuzaev,
  • R. Ch. Kulaev

摘要

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.