The basis property of generalized eigenfunctions for one boundary value problem with discontinuities at two interior points

Year 2024, Volume: 13 Issue: 3, 221 - 231, 31.12.2024

Hayati Olğar , Oktay Mukhtarov

https://doi.org/10.54187/jnrs.1569468

Abstract

In this study, we consider a spectral problem for one boundary value problem with discontinuities at two interior points. The boundary conditions involve a spectral parameter. We consider some compact, positive, self-adjoint operators to reduce the spectral problem to an operator-pencil equation. Then, it was proven that this operator-pencil is positive definite, the spectrum is discrete, and the system of weak eigenfunctions forms a Riesz basis of the appropriate Sobolev space.

Keywords

Spectral problem, Boundary conditions, Jump conditions, Eigenvalues, Weak eigenfunctions

Ethical Statement

No approval from the Board of Ethics is required.

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