The weak eigenfunctions of boundary-value problem with symmetric discontinuities-Reference-Cited by-同舟云学术

The weak eigenfunctions of boundary-value problem with symmetric discontinuities

Published:2022-01-28 Issue:2 Volume:28 Page:275-283
ISSN:1425-6908
Container-title:Journal of Applied Analysis
language:en
Short-container-title:

Author:

Olğar Hayati¹^ORCID,Mukhtarov Oktay S.²^ORCID,Muhtarov Fahreddin S.³^ORCID,Aydemir Kadriye⁴^ORCID

Affiliation:

1. Department of Mathematics , Faculty of Science , Tokat Gaziosmanpaşa University , Tokat , Turkey

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

3. Institute of Mathematics and Mechanics , National Academy of Sciences , Baku , Azerbaijan

4. Department of Mathematics , Faculty of Arts and Science , Amasya University , Amasya , Turkey

Abstract

Abstract 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.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Computational Theory and Mathematics,Statistics, Probability and Uncertainty,Mathematical Physics

Link

https://www.degruyter.com/document/doi/10.1515/jaa-2021-2079/pdf

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