Geodesic
The finiteness of the spectrum of boundary value problems defined on a geometric graph
Trudy Moskovskogo matematičeskogo obŝestva, Trudy Moskovskogo Matematicheskogo Obshchestva, Tome 80 (2019) no. 2, pp. 147-156

Voir la notice de l'article provenant de la source Math-Net.Ru

We consider boundary value problems on a geometric graph with a polynomial occurrence of spectral parameter in the differential equation. It has previously been shown (see A. M. Akhtyamov [Differ. Equ.55 (2019), no. 1, pp. 142-144]) that a boundary value problem for one differential equation whose characteristic equation has simple roots cannot have a finite spectrum, and a boundary value problem for one differential equation can have any given finite spectrum when the characteristic polynomial has multiple roots. In this paper, we obtain a similar result for differential equations defined on a geometric graph. We show that a boundary value problem on a geometric graph cannot have a finite spectrum if all its characteristic equations have simple roots, and a boundary value problem has a finite spectrum if at least one characteristic equation has multiple roots. We also give results showing that a boundary value problem can have any given finite spectrum. 
@article{MMO_2019_80_2_a1,
     author = {V. A. Sadovnichii and Ya. T. Sultanaev and A. M. Akhtyamov},
     title = {The finiteness of the spectrum of boundary value problems defined on a geometric graph},
     journal = {Trudy Moskovskogo matemati\v{c}eskogo ob\^{s}estva},
     pages = {147--156},
     publisher = {mathdoc},
     volume = {80},
     number = {2},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MMO_2019_80_2_a1/}
}
TY  - JOUR
AU  - V. A. Sadovnichii
AU  - Ya. T. Sultanaev
AU  - A. M. Akhtyamov
TI  - The finiteness of the spectrum of boundary value problems defined on a geometric graph
JO  - Trudy Moskovskogo matematičeskogo obŝestva
PY  - 2019
SP  - 147
EP  - 156
VL  - 80
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MMO_2019_80_2_a1/
LA  - ru
ID  - MMO_2019_80_2_a1
ER  - 
%0 Journal Article
%A V. A. Sadovnichii
%A Ya. T. Sultanaev
%A A. M. Akhtyamov
%T The finiteness of the spectrum of boundary value problems defined on a geometric graph
%J Trudy Moskovskogo matematičeskogo obŝestva
%D 2019
%P 147-156
%V 80
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MMO_2019_80_2_a1/
%G ru
%F MMO_2019_80_2_a1
V. A. Sadovnichii; Ya. T. Sultanaev; A. M. Akhtyamov. The finiteness of the spectrum of boundary value problems defined on a geometric graph. Trudy Moskovskogo matematičeskogo obŝestva, Trudy Moskovskogo Matematicheskogo Obshchestva, Tome 80 (2019) no. 2, pp. 147-156. http://geodesic.mathdoc.fr/item/MMO_2019_80_2_a1/