Criteria for the uniqueness of a solution for some differential-operator equation

Baltabek  Kanguzhin; Bakytbek Koshanov

doi:10.70474/2pmhkg48

Авторы

Балтабек Есматович Кангужин Казахский национальный университет имени аль-Фараби Автор https://orcid.org/0000-0001-5504-6362
Бакытбек Данебекович Кошанов Институт математики и математического моделирования Автор https://orcid.org/0000-0002-0784-5183

DOI:

https://doi.org/10.70474/2pmhkg48

Ключевые слова:

симметричные операторы, уравнение Штурма-Лиувилля, невырожденные граничные условия, единственность решения, собственные значения оператора, полные ортогональные системы, спектр оператора

Аннотация

В данной статье симметричный оператор L, соответствующий краевой задаче, представляется в виде разности двух коммутирующих операторов A и B.
Единственность решения операторного уравнения Lu = (B–A)u = 0 гарантируется, если спектры операторов A и B не пересекаются и область определения оператора B задана невырожденными граничными условиями. В отличие от существующих результатов работ, сформулированный в данной статье критерий единственности краевой задачи выполняется даже в том случае, когда система корневых функций оператора B не образует базиса в соответствующем пространстве. При этом требуется лишь замкнутость линейного оператора A.

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