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The finiteness of the spectrum of boundary value problems defined on a geometric graphстатья
Информация о цитировании статьи получена из
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Статья опубликована в журнале из списка Web of Science и/или Scopus
Дата последнего поиска статьи во внешних источниках: 20 января 2021 г.
- Авторы: Sadovnichii V.A., Sultanaev Ya T., Akhtyamov A.M.
- Журнал: Transactions of the Moscow Mathematical Society
- Том: 80
- Год издания: 2019
- Первая страница: 123
- Последняя страница: 131
- DOI: 10.1090/mosc/293
- Аннотация: 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 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.
- Добавил в систему: Садовничий Виктор Антонович