Abstract
The purpose of this paper is to study a Sturm–Liouville problem with discontinuities in the case when an eigenparameter appears not only in the differential equation but it also appears in both the boundary and transmission conditions.
We suggest a new approach for the definition of a suitable Hilbert space and a symmetric linear operator defined in this space in such a way that the considered problem can be interpreted as the eigenvalue problem of this operator and for construction and approximation of a fundamental solution. We apply these results to find asymptotic formulas of eigenvalues and corresponding eigenfunctions.
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Mathematics Subject Classification (2000)
34L20.
This work was supported by the Research Fund of Gaziosmanpasa University under grand no:2004/01.
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Akdoğan, Z., Demirci, M. & Mukhtarov, O.S. Discontinuous Sturm–Liouville Problems with Eigenparameter-Dependent Boundary and Transmissions Conditions. Acta Appl Math 86, 329–344 (2005). https://doi.org/10.1007/s10440-004-7466-3
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DOI: https://doi.org/10.1007/s10440-004-7466-3