图上四阶微分算子特征值乘数的上界

IF 0.58 Q3 Engineering

Journal of Applied and Industrial Mathematics Pub Date : 2024-08-15 DOI:10.1134/S1990478924020169

A. A. Urtaeva

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引用次数: 0

摘要

摘要本文研究了一个平面梁结构模型，该模型由几何图上的四阶边界值问题描述。在图的内部顶点提出了弹性铰链连接条件。我们研究了相应谱问题谱点的性质，证明了特征值乘数的上界，并表明特征值乘数取决于图形结构（边界顶点数、循环数等）。我们举例说明了我们的估计值是尖锐的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Upper Bounds for the Eigenvalue Multiplicities of a Fourth-Order Differential Operator on a Graph

The paper studies a model of a planar beam structure described by a fourth-order boundary value problem on a geometric graph. Elastic-hinge joint conditions are posed at the interior vertices of the graph. We study the properties of the spectral points of the corresponding spectral problem, prove upper bounds for the eigenvalue multiplicities, and show that the eigenvalue multiplicities depend on the graph structure (the number of boundary vertices, cycles, etc.). We give an example showing that our estimates are sharp.

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来源期刊

Journal of Applied and Industrial Mathematics Engineering-Industrial and Manufacturing Engineering

CiteScore

1.00

自引率

0.00%

发文量

期刊介绍： Journal of Applied and Industrial Mathematics is a journal that publishes original and review articles containing theoretical results and those of interest for applications in various branches of industry. The journal topics include the qualitative theory of differential equations in application to mechanics, physics, chemistry, biology, technical and natural processes; mathematical modeling in mechanics, physics, engineering, chemistry, biology, ecology, medicine, etc.; control theory; discrete optimization; discrete structures and extremum problems; combinatorics; control and reliability of discrete circuits; mathematical programming; mathematical models and methods for making optimal decisions; models of theory of scheduling, location and replacement of equipment; modeling the control processes; development and analysis of algorithms; synthesis and complexity of control systems; automata theory; graph theory; game theory and its applications; coding theory; scheduling theory; and theory of circuits.