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On the second largest multiplicity of eigenvalues for the Stieltjes string spectral problem on trees


Abstract

The largest possible multiplicity of an eigenvalue of a spectral problem generated by the Stieltjes string equations on a metric tree is $p_{pen}-1$, where $p_{pen}$ is the number of pendant vertices. We propose how to find the second largest possible multiplicity of an eigenvalue of such a problem. This multiplicity depends on the numbers of point masses on the edges of the trees.

Максимально можлива кратність власного значення спектральної задачі, породженої рівняннями струни Стілтьєса на метричному дереві, дорівнює $p_{pen}-1$, де $p_{pen}$ — кількість висячих вершин. Ми пропонуємо, як знайти другу за величиною кратність власного значення такої задачі. Ця кратність залежить від кількості точкових мас на ребрах дерев.

Key words: Stieltjes string equation, difference equations on tree graphs, Dirichlet boundary condition, boundary value problem, spectrum, vertex degree.


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Article Information

TitleOn the second largest multiplicity of eigenvalues for the Stieltjes string spectral problem on trees
SourceMethods Funct. Anal. Topology, Vol. 27 (2021), no. 3, 217-226
DOI10.31392/MFAT-npu26_3.2021.03
MilestonesReceived 29/05/2020; Revised 08/07/2021
CopyrightThe Author(s) 2021 (CC BY-SA)

Authors Information

Olga Boyko
Department of Applied Mathematics and Computer Science, South Ukrainian National Pedagogical University, Odesa, Ukraine

Olga Martynyuk
Department of Higher Mathematics and Statistics, South Ukrainian National Pedagogical University, Odesa, Ukraine

Vyacheslav Pivovarchik
Department of Higher Mathematics and Statistics, South Ukrainian National Pedagogical University, Odesa, Ukraine


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Citation Example

Olga Boyko, Olga Martynyuk, and Vyacheslav Pivovarchik, On the second largest multiplicity of eigenvalues for the Stieltjes string spectral problem on trees, Methods Funct. Anal. Topology 27 (2021), no. 3, 217-226.


BibTex

@article {MFAT1629,
    AUTHOR = {Olga Boyko and Olga Martynyuk and Vyacheslav Pivovarchik},
     TITLE = {On the second largest multiplicity of eigenvalues for the Stieltjes
  string spectral problem on
  trees},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {27},
      YEAR = {2021},
    NUMBER = {3},
     PAGES = {217-226},
      ISSN = {1029-3531},
       DOI = {10.31392/MFAT-npu26_3.2021.03},
       URL = {http://mfat.imath.kiev.ua/article/?id=1629},
}


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