The weak eigenfunctions of boundary-value problem with symmetric discontinuities
-
Hayati Olğar
,
Oktay S. Mukhtarov
,
Fahreddin S. Muhtarov
and
Kadriye Aydemir
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.
Funding statement: This study was presented partially in ISAS 2018 (2nd International Symposium on Innovative Approaches in Scientific Studies).
Acknowledgements
The authors would like to thank the anonymous reviewers and editorial team for their valuable comments, suggestions and contributions.
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