The weak eigenfunctions of boundary-value problem with symmetric discontinuities

• Autorzy: Olğar Hayati , Mukhtarov Oktay S. , Muhtarov Fahreddin S. , Aydemir Kadriye

Identyfikatory

DOI

10.1515/jaa-2021-2079

• Języki publikacji: EN

Abstrakty

EN

The main goal of this study is the investigation of discontinuous boundary-value problems for second-order differential operators with symmetric transmission conditions.We introduce the new notion of weak functions for such type of discontinuous boundary-value problems and develop an operator-theoretic method for the investigation of the spectrum and completeness property of the weak eigenfunction systems. In particular, we define some self-adjoint compact operators in suitable Sobolev spaces such that the considered problem can be reduced to an operator-pencil equation. The main result of this paper is that the spectrum is discrete and the set of eigenfunctions forms a Riesz basis of the suitable Hilbert space.

Słowa kluczowe

EN

boundary value problems; transmission conditions; weak eigenfunctions; eigenvalue; completeness; Riesz basis

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2022
• Tom: Vol. 28, nr 2
• Strony: 275--283
• Opis fizyczny: Bibliogr. 26 poz.

Twórcy

autor

Olğar Hayati

• Department of Mathematics, Faculty of Science, Tokat Gaziosmanpaşa University, Tokat, Turkey

• https://orcid.org/0000-0003-4732-1605

autor

Mukhtarov Oktay S.

• Department of Mathematics, Faculty of Science, Tokat Gaziosmanpaşa University, Tokat, Turkey
• Institute of Mathematics and Mechanics, National Academy of Sciences, Baku, Azerbaijan

• https://orcid.org/0000-0001-7480-6857

autor

Muhtarov Fahreddin S.

• Institute of Mathematics and Mechanics, National Academy of Sciences, Baku, Azerbaijan

• https://orcid.org/0000-0002-5482-2478

autor

Aydemir Kadriye

• Department of Mathematics, Faculty of Arts and Science, Amasya University, Amasya, Turkey

• https://orcid.org/0000-0002-8378-3949

Bibliografia

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Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2024).