| Volume 7, Number 2, 2017, Pages 559-580 DOI：10.11948/2017035 |
| Inverse problems for the Sturm-Liouville equation with the discontinuous coefficient |
| Anar Adiloglu Nabiev,Mehmet Gurdal,Suna Saltan |
| Keywords:Sturm-Louville equation, boundary value problems, spectral analysis of ordinary differential operators, transformation operator, integral representation, asymptotic formulas for eigenvalues, expansion formula. |
| Abstract: |
| In this study we derive the Gelfand-Levitan-Marchenko type main integral equation of the inverse problem for the boundary value problem $L$ and prove the uniquely solvability of the main integral equation. Further, we give the solution of the inverse problem by the spectral data and by two spectrum. |
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