Abstract
In this article, we study the wellposedness of the inverse problem for Sturm-Liouville equation with coulomb potential. We will consider two different inverse problem for Sturm-Liouville equation with coulomb potential. We will prove that ıf the spectral characteristics of this problems are close to each other, then the difference between their potential functions is sufficiently small.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Ambarzumjan, V.A.: Eine umkehrung der Sturm-Liouvillischen eigen wertaufgabe. Acta Math. 78, 1–96 (1946)
Amirov, R.K., Cakmak, Y.: Trace Formula for the Sturm-Liouville operator with singularity. In: Proceeding of the Eight International Colloquium on differential equations, Plovdiv, Bulgaria, pp. 9–16 (1997)
Bas, E., Panakhov, E., Yilmazer, R.: The uniqueness theorem for hydrogen atom equation. TWMS J. Pure Appl. Math. 4(1), 20–28 (2013)
Freeling, G., Ryklov, V., Yurko, V.: Spectral analysis for an indefinite singular Sturm-Liouville problem. Appl. Anal. 81, 1283–1305 (2002)
Gelfand, I.M., Levitan, B.M.: On the determination of a differential equation by its spectral function. Izv. Nauk SSSR Ser. Math. 15, 309–360 (1951). (Ams, (1955) 253-304)
Guldu, Y., Mise, E.: On Dirac operator with boundary and transmission conditions depending Herglotz-Nevanlinna type function. AIMS Math. 6(4), 3686–3703 (2021)
Guliyev, N.J.: Inverse eigenvalue problems for Sturm-Liouville equations with spectral parameter linearly contained in one of the boundary conditions. Inverse Prob. 21(4), 1315 (2005)
Gasymov, M.G.: On the determination of the Sturm -Liouville equation with peculiarity in zero peculiarity in zero on two spectrum. DAN SSSR 161(2), 271–276 (1965)
Hryniv, O.R., Mykytyuk, Y.V.: Half inverse problem for Sturm-Liouville operators with singular potentials. Inverse Prob. 20, 1423–1444 (2004)
Levitan, B.M.: On the determination of the Sturm-Liouville operator from one and two spectra. Math. USSR Izvest. 12, 179–193 (1978)
Mizutani, A.: On the inverse Sturm-Liouville problem. J. Fac. Sci. Univ. Tokyo Sect. IA Math. 31, 319–350 (1984)
Marchenko, V.A.: Sturm-Liouville Operators and Applications. Birhkauser, Basel (1886)
Marchenko, V.A.: Some problems in the theory of second-order differential operators. Dokl. Akad. Nauk SSSR 72, 457–560 (1950)
Mukhtarov, O.S., Aydemir, K.: Discontinuous Sturm-Liouville problems involving an abstract linear operator. J. Appl. Anal. Comput. 10(4), 1545–1560 (2020)
Mukhtarov, O.S., Aydemir, K.: Oscillation properties for non-classical Sturm-Liouville problems with additional transmission conditions. Math. Model. Anal. 26(3), 432–443 (2021)
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Kayalar, M. A uniqueness theorem for singular Sturm-liouville operator. Afr. Mat. 34, 59 (2023). https://doi.org/10.1007/s13370-023-01097-x
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s13370-023-01097-x