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

Yıl 2012, Cilt 33, Sayı 2, 1 - 7, 21.02.2013

Öz

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).

Kaynakça

  • Hochstadt, H. and Lieberman, B., An Inverse Sturm-Liouville Problem with Mixed Given Data, SIAM J. Appl. Math., 1978; 34: 676-680.
  • Hald, O. H., Discontinuous inverse eigenvalue problems, Comm. Pure Appl. Math., 1984, 37; 59-577.
  • 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.
  • 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.
  • Sakhnovic, L., Half inverse problems on the finite interval, Inverse Problems 17, 2001; 527-532.
  • 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.
  • Koyunbakan, H., Panakhov, E.S., Half-inverse problem for diffusion operators on the finite interval, J. Math. anal. Appl., 2007; 326 , 1024–1030.
  • 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.
  • 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.
  • Marchenko, V. A., Sturm-Liouville Operators and Their Applications, Naukova Dumka, Kiev, English transl.: Birkhauser, Basel, 1986,.
  • 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),

Yıl 2012, Cilt 33, Sayı 2, 1 - 7, 21.02.2013

Öz

Kaynakça

  • Hochstadt, H. and Lieberman, B., An Inverse Sturm-Liouville Problem with Mixed Given Data, SIAM J. Appl. Math., 1978; 34: 676-680.
  • Hald, O. H., Discontinuous inverse eigenvalue problems, Comm. Pure Appl. Math., 1984, 37; 59-577.
  • 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.
  • 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.
  • Sakhnovic, L., Half inverse problems on the finite interval, Inverse Problems 17, 2001; 527-532.
  • 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.
  • Koyunbakan, H., Panakhov, E.S., Half-inverse problem for diffusion operators on the finite interval, J. Math. anal. Appl., 2007; 326 , 1024–1030.
  • 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.
  • 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.
  • Marchenko, V. A., Sturm-Liouville Operators and Their Applications, Naukova Dumka, Kiev, English transl.: Birkhauser, Basel, 1986,.
  • 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),

Ayrıntılar

Birincil Dil İngilizce
Bölüm Editöriyal
Yazarlar

Nilüfer TOPSAKAL
0000-0001-7216-044X


Rauf AMİROV


Nilüfer TOPSAKAL
0000-0001-7216-044X


Yalçın GÜLDÜ


Rauf AMİROV

Yayımlanma Tarihi 21 Şubat 2013
Yayınlandığı Sayı Yıl 2012, Cilt 33, Sayı 2

Kaynak Göster

Bibtex @ { cumuscij57943, journal = {Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi}, issn = {1300-1949}, eissn = {1300-1949}, address = {}, publisher = {Sivas Cumhuriyet Üniversitesi}, year = {2013}, volume = {33}, pages = {1 - 7}, doi = {}, title = {Half inverse problem for singular Sturm-Liouville operators with discontinuity conditions inside an interval}, key = {cite}, author = {Topsakal, Nilüfer and Amirov, Rauf and Topsakal, Nilüfer and Güldü, Yalçın and Amirov, Rauf} }
APA Topsakal, N. , Amirov, R. , Topsakal, N. , Güldü, Y. & Amirov, R. (2013). Half inverse problem for singular Sturm-Liouville operators with discontinuity conditions inside an interval . Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi , 33 (2) , 1-7 . Retrieved from https://dergipark.org.tr/tr/pub/cumuscij/issue/4325/57943
MLA Topsakal, N. , Amirov, R. , Topsakal, N. , Güldü, Y. , Amirov, R. "Half inverse problem for singular Sturm-Liouville operators with discontinuity conditions inside an interval" . Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi 33 (2013 ): 1-7 <https://dergipark.org.tr/tr/pub/cumuscij/issue/4325/57943>
Chicago Topsakal, N. , Amirov, R. , Topsakal, N. , Güldü, Y. , Amirov, R. "Half inverse problem for singular Sturm-Liouville operators with discontinuity conditions inside an interval". Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi 33 (2013 ): 1-7
RIS TY - JOUR T1 - Half inverse problem for singular Sturm-Liouville operators with discontinuity conditions inside an interval AU - Nilüfer Topsakal , Rauf Amirov , Nilüfer Topsakal , Yalçın Güldü , Rauf Amirov Y1 - 2013 PY - 2013 N1 - DO - T2 - Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi JF - Journal JO - JOR SP - 1 EP - 7 VL - 33 IS - 2 SN - 1300-1949-1300-1949 M3 - UR - Y2 - 2022 ER -
EndNote %0 Cumhuriyet Üniversitesi Fen-Edebiyat Fakültesi Fen Bilimleri Dergisi Half inverse problem for singular Sturm-Liouville operators with discontinuity conditions inside an interval %A Nilüfer Topsakal , Rauf Amirov , Nilüfer Topsakal , Yalçın Güldü , Rauf Amirov %T Half inverse problem for singular Sturm-Liouville operators with discontinuity conditions inside an interval %D 2013 %J Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi %P 1300-1949-1300-1949 %V 33 %N 2 %R %U
ISNAD Topsakal, Nilüfer , Amirov, Rauf , Topsakal, Nilüfer , Güldü, Yalçın , Amirov, Rauf . "Half inverse problem for singular Sturm-Liouville operators with discontinuity conditions inside an interval". Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi 33 / 2 (Şubat 2013): 1-7 .
AMA Topsakal N. , Amirov R. , Topsakal N. , Güldü Y. , Amirov R. Half inverse problem for singular Sturm-Liouville operators with discontinuity conditions inside an interval. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi. 2013; 33(2): 1-7.
Vancouver Topsakal N. , Amirov R. , Topsakal N. , Güldü Y. , Amirov R. Half inverse problem for singular Sturm-Liouville operators with discontinuity conditions inside an interval. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi. 2013; 33(2): 1-7.
IEEE N. Topsakal , R. Amirov , N. Topsakal , Y. Güldü ve R. Amirov , "Half inverse problem for singular Sturm-Liouville operators with discontinuity conditions inside an interval", Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi, c. 33, sayı. 2, ss. 1-7, Şub. 2013