On multiplicity of eigenvalues in quantum graph theory

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:480

Article

Pivovarchik, V.¹ 

[1] South Ukrainian Natl Pedag Univ, Staroportofrankovskaya Str 26, UA-65020 Odessa, Ukraine

关键词: Dirichlet boundary condition;    Neumann boundary condition;    Kirchhoff's condition;    Spectrum;    Tree;   

DOI  :  10.1016/j.jmaa.2019.123412

来源: Elsevier

【 摘 要 】

Spectral problems are considered generated by the Sturm-Liouville equation on equilateral trees with the Dirichlet boundary conditions at pendant vertices and continuity and Kirchhoff's conditions at interior vertices. It is shown that the eigenvalues of such problems approach asymptotically the eigenvalues of the problem on the same tree with zero potentials on the edges. It is shown that between any two eigenvalues of maximal multiplicity (p(pen)-1) where p(pen) is the number of pendant vertices there are p(in) eigenvalues (with account of multiplicity, where p(in) is the number of interior vertices in the tree). (C) 2019 Published by Elsevier Inc.

【 授权许可】

Free