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

Nilüfer Topsakal; Rauf Amirov; Nilüfer Topsakal; Yalçın Güldü; Rauf Amirov

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

Year 2012, Volume: 33 Issue: 2, 1 - 7, 21.02.2013

Nilüfer Topsakal , Rauf Amirov , Nilüfer Topsakal , Yalçın Güldü , Rauf Amirov

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).

Keywords

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References

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),

Year 2012, Volume: 33 Issue: 2, 1 - 7, 21.02.2013

Nilüfer Topsakal , Rauf Amirov , Nilüfer Topsakal , Yalçın Güldü , Rauf Amirov

Abstract

References

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),

There are 11 citations in total.

Details

Primary Language	English
Journal Section	Editorial
Authors	Nilüfer Topsakal Rauf Amirov Nilüfer Topsakal Yalçın Güldü Rauf Amirov
Publication Date	February 21, 2013
Published in Issue	Year 2012 Volume: 33 Issue: 2

Cite

APA	Topsakal, N., Amirov, R., Topsakal, N., Güldü, Y., et al. (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.
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. February 2013;33(2):1-7.
Chicago	Topsakal, Nilüfer, Rauf Amirov, Nilüfer Topsakal, Yalçın Güldü, and Rauf Amirov. “Half Inverse Problem for Singular Sturm-Liouville Operators With Discontinuity Conditions Inside an Interval”. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi 33, no. 2 (February 2013): 1-7.
EndNote	Topsakal N, Amirov R, Topsakal N, Güldü Y, Amirov R (February 1, 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.
IEEE	N. Topsakal, R. Amirov, N. Topsakal, Y. Güldü, and R. Amirov, “Half inverse problem for singular Sturm-Liouville operators with discontinuity conditions inside an interval”, Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi, vol. 33, no. 2, pp. 1–7, 2013.
ISNAD	Topsakal, Nilüfer et al. “Half Inverse Problem for Singular Sturm-Liouville Operators With Discontinuity Conditions Inside an Interval”. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi 33/2 (February 2013), 1-7.
JAMA	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;33:1–7.
MLA	Topsakal, Nilüfer et al. “Half Inverse Problem for Singular Sturm-Liouville Operators With Discontinuity Conditions Inside an Interval”. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi, vol. 33, no. 2, 2013, pp. 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.