Inverse Sturm-Liouville problems with two supplementary discontinuous conditions on two symmetric disjoint intervals. (English) Zbl 1474.34089
Summary: In this paper, we consider Sturm-Liouville problems on two symmetric disjoint intervals with two supplementary discontinuous conditions at an interior point. First, we investigate some spectral properties of boundary value problems, and obtain the asymptotic form of the eigenvalues and the eigenfunctions. Then, the eigenfunction expansion of Green’s function is presented and we prove the uniqueness theorems for the solution of the inverse problem, and reconstruct the Sturm-Liouville operator and the coefficients of boundary conditions using the Weyl \(m\)-function and spectral data. Also, numerical examples are presented.
MSC:
| 34A55 | Inverse problems involving ordinary differential equations |
| 34L10 | Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators |
| 34B24 | Sturm-Liouville theory |
| 34L20 | Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions for ordinary differential operators |
Keywords:
inverse Sturm-Liouville problems; discontinuous conditions; Green’s function; expansion theorem; Weyl \(m\)-functionReferences:
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