{"title":"Upper Bounds for the Eigenvalue Multiplicities\nof a Fourth-Order Differential Operator on a Graph","authors":"A. A. Urtaeva","doi":"10.1134/S1990478924020169","DOIUrl":null,"url":null,"abstract":"<p> The paper studies a model of a planar beam structure described by a fourth-order\nboundary value problem on a geometric graph. Elastic-hinge joint conditions are posed at the\ninterior vertices of the graph. We study the properties of the spectral points of the corresponding\nspectral problem, prove upper bounds for the eigenvalue multiplicities, and show that the\neigenvalue multiplicities depend on the graph structure (the number of boundary vertices, cycles,\netc.). We give an example showing that our estimates are sharp.\n</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":"18 2","pages":"352 - 360"},"PeriodicalIF":0.5800,"publicationDate":"2024-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied and Industrial Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1134/S1990478924020169","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Engineering","Score":null,"Total":0}
引用次数: 0
Abstract
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.
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.
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