INVERSE PROBLEMS FOR THE STURM-LIOUVILLE EQUATION WITH THE DISCONTINUOUS COEFFICIENT

Anar Adiloglu Nabiev; Mehmet Gürdal; Suna Saltan

doi:10.11948/2017035

2017 Volume 7 Issue 2

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Anar Adiloglu Nabiev, Mehmet Gürdal, Suna Saltan. INVERSE PROBLEMS FOR THE STURM-LIOUVILLE EQUATION WITH THE DISCONTINUOUS COEFFICIENT[J]. Journal of Applied Analysis & Computation, 2017, 7(2): 559-580. doi: 10.11948/2017035

Citation:

Anar Adiloglu Nabiev, Mehmet Gürdal, Suna Saltan. INVERSE PROBLEMS FOR THE STURM-LIOUVILLE EQUATION WITH THE DISCONTINUOUS COEFFICIENT[J]. Journal of Applied Analysis & Computation, 2017, 7(2): 559-580. doi: 10.11948/2017035

INVERSE PROBLEMS FOR THE STURM-LIOUVILLE EQUATION WITH THE DISCONTINUOUS COEFFICIENT

1 Department of Mathematics, Faculty of Science, Cumhuriyet University, 58140 Sivas, Turkey;
2 Department of Mathematics, Faculty of Science, Suleyman Demirel University, 32260, Isparta, Turkey

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Abstract

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.
- Sturm-Louville equation /
- boundary value problems /
- spectral analysis of ordinary differential operators /
- transformation operator /
- integral representation /
- asymptotic formulas for eigenvalues /
- expansion formula
MSC: 34L40;34B24;34L05

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References

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