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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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