The weak eigenfunctions of boundary-value problem with symmetric discontinuities

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-theor...

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Bibliographic Details
Published in:Journal of applied analysis 2022-12, Vol.28 (2), p.275-283
Main Authors: Olğar, Hayati, Mukhtarov, Oktay S., Muhtarov, Fahreddin S., Aydemir, Kadriye
Format: Article
Language:English
Subjects:
34B24
34L10
34L15 34B08
Applied mathematics
Boundary conditions
Boundary value problems
completeness
Differential equations
Discontinuity
eigenvalue
Eigenvalues
Eigenvectors
Engineering
Hilbert space
Linear operators
Mathematical analysis
Operators (mathematics)
Physics
Riesz basis
Science
Sobolev space
transmission conditions
weak eigenfunctions
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Summary: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.
ISSN:1425-6908
1869-6082
DOI:10.1515/jaa-2021-2079