Half inverse problem for singular Sturm-Liouville operators with discontinuity conditions inside an interval
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).
Anahtar Kelimeler
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),
Toplam 11 adet kaynakça vardır.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Bölüm | Editöriyal |
| Yazarlar | |
| Yayımlanma Tarihi | 21 Şubat 2013 |
| Yayımlandığı Sayı | Yıl 2012 Cilt: 33 Sayı: 2 |