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Open Access Research

Inverse eigenvalue problems for a discontinuous Sturm-Liouville operator with two discontinuities

Yalçın Güldü

Author Affiliations

Department of Mathematics, Faculty of Sciences, Cumhuriyet University, Sivas, 58140, Turkey

Boundary Value Problems 2013, 2013:209  doi:10.1186/1687-2770-2013-209

Published: 11 September 2013

Abstract

In this paper, we consider a discontinuous Sturm-Liouville operator with parameter-dependent boundary conditions and two interior discontinuities. We obtain eigenvalues and eigenfunctions together with their asymptotic approximate formulas. Then, we give some uniqueness theorems by using Weyl function and spectral data, which are called eigenvalues and normalizing constants for solution of inverse problem.

MSC: 34A55, 34B24, 34L05.

Keywords:
Sturm-Liouville problem; eigenvalues; eigenfunctions; transmission conditions; Weyl function