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Dergiler / Cumhuriyet Science Journal / 2012 / Cilt: 33 - Sayı: 2

Half inverse problem for singular Sturm-Liouville operators with discontinuity conditions inside an interval

Nilüfer TOPSAKAL
Rauf AMİROV
Nilüfer TOPSAKAL
Yalçın GÜLDÜ
Rauf AMİROV
Sayfa
1–7
Yayın Tarihi
2013-02-21
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

It is shown by Hochstadt and Lieberman's method that if the potential function q(x) prescribed on interval ((π/2),π), then a single spectrum sufficies to determine q(x) on the whole interval (0,π).

📌 3 Maddede Bu Makale

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Amaç & Hipotez:In this study, half inverse problem for singular Sturm-Liouville operator is considered.
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Temel Bulgular & Veri:In this study, half inverse problem for singular Sturm-Liouville operator is considered.
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Sonuç & Katkı:It is shown by Hochstadt and Lieberman's method that if the potential function q(x) prescribed on interval ((π/2),π), then a single spectrum sufficies to determine q(x) on the whole interval (0,π).
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri

Abstract

In this study, half inverse problem for singular Sturm-Liouville operator is considered. It is shown by Hochstadt and Lieberman's method that if the potential function q(x) prescribed on interval ((π/2),π), then a single spectrum sufficies to determine q(x) on the whole interval (0,π).

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Bu Makaleye Atıf Yap

TOPSAKAL, N., AMİROV, R., TOPSAKAL, N., GÜLDÜ, Y., AMİROV, R. (2013). Half inverse problem for singular Sturm-Liouville operators with discontinuity conditions inside an interval. Cumhuriyet Science Journal, Cilt: 33 - Sayı: 2, 1–7. https://ajindex.com/articles/483009

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Kaynakça (11)

  1. Hochstadt, H. and Lieberman, B., An Inverse Sturm-Liouville Problem with Mixed Given Data, SIAM J. Appl. Math., 1978; 34: 676-680.
  2. Hald, O. H., Discontinuous inverse eigenvalue problems, Comm. Pure Appl. Math., 1984, 37; 59-577.
  3. Malamud, M.M., Uniqueness questions in inverse problems for systems of differential equations on a finite interval, Trans. Moscow Math. Soc., 1999, 60; 204-262.
  4. Gesztesy, F., Simon, B., Inverse spectral analysis with partial information on the potential II, The case of discrete spectrum. Transactions in American Mathematical Society, 2000, 352; 2765-2789.
  5. Sakhnovic, L., Half inverse problems on the finite interval, Inverse Problems 17, 2001; 527-532.
  6. Hryniv, O.R., Myktyuk, Y.V., Half-inverse spectral problems for Sturm-Liouville op- erators with singular potentials, Inverse Problems, 2004; 20(5), 1423-1444.
  7. Koyunbakan, H., Panakhov, E.S., Half-inverse problem for diffusion operators on the finite interval, J. Math. anal. Appl., 2007; 326, 1024–1030.
  8. Borg, G., Eine umkehrung der Sturm-Liouvillesehen eigenwertaufgabe, Acta Math., 1945; 78, 1-96. [9] Naimark, M. A., Linear Differential Operators, Moscow, Nauka, (in Russian) 1967.
  9. R. Kh. Amirov, Transformation operator for Sturm-Liouville Operators with singular- ity and discontinuity conditions inside an interval, Trans.of NAS of Azerbajian, 2006; 35-54.
  10. Marchenko, V. A., Sturm-Liouville Operators and Their Applications, Naukova Dumka, Kiev, English transl.: Birkhauser, Basel, 1986,.
  11. Guldu, Y., Amirov, R. Kh. and Topsakal, N., On impulsive Sturm-Liouville opera- tors with singularity and spectral parameter in boundary conditions. J. of Ukrainian Mathematical, 2012 (to appear),