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.
Full Text
Article Information
| Title | On the second largest multiplicity of eigenvalues for the Stieltjes
string spectral problem on
trees |
| Source | Methods Funct. Anal. Topology, Vol. 27 (2021), no. 3, 217-226 |
| DOI | 10.31392/MFAT-npu26_3.2021.03 |
| MathSciNet |
MR4344362 |
| Milestones | Received 29/05/2020; Revised 08/07/2021 |
| Copyright | The 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
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},
MRNUMBER = {MR4344362},
DOI = {10.31392/MFAT-npu26_3.2021.03},
URL = {http://mfat.imath.kiev.ua/article/?id=1629},
}
