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Inverse problems for the Sturm-Liouville equation with the discontinuous coefficient |
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| Authors: | Anar Adiloglu Nabiev Mehmet Gurdal Suna Saltan |
| Affiliation: | Department of Mathematics, Faculty of Science, Cumhuriyet University, 58140 Sivas, Turkey,Department of Mathematics, Faculty of Science, Suleyman Demirel University, 32260, Isparta, Turkey and Department of Mathematics, Faculty of Science, Suleyman Demirel University, 32260, Isparta, Turkey |
| 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. |
| Keywords: | Sturm-Louville equation boundary value problems spectral analysis of ordinary differential operators transformation operator integral representation asymptotic formulas for eigenvalues expansion formula. |
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