Abstract
We study the inverse spectral problems for second-order differential equations on a finite interval having regular singularities inside the interval. Necessary and sufficient conditions for the solvability of these inverse problems and a procedure for the solution of these problems are given, and uniqueness theorems are proved.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Marchenko V. A., Sturm—Liouville operators and their applications, Naukova Dumka, Kiev, 1977; English transi., Birkhauser, 1986.
Levitan B. M., Inverse Sturm—Liouville problems, Nauka, Moscow, 1984; English transi., VNU Sci. Press, Utrecht, 1987.
McLaughlin J. R., Analytical methods for recovering coefficients in differential equations from spectral data, SIAM Rev. 28 (1986), 53–72.
Stashevskaya V. V., On inverse problems of spectral analysis for a certain class of differential equations, Dokl. Akad. Nauk SSSR 93 (1953), 409–412.
Gasymov M. G., Determination of Sturm—Liouville equation with a singular point from two spectra, Dokl. Akad. Nauk SSSR 161 (1965), 274–276.
Carlson R., Inverse spectral theory for some singular Sturm—Liouville problems, J. Diff. Equations 106 (1993), 121–140.
Zhornitskaya L. A. and Serov V. S., Inverse eigenvalue problems for a singular Sturm—Liouville operator on (0,1), Inverse Problems 10 (1994), no.4, 975–987.
Yurko V. A., Inverse problem for differential equations with a singularity, Differentsialnye Uravneniya 28 (1992), 1355–1362; English transl. in Differential Equations 28 (1992), 1100-1107.
Yurko V. A., On higher-order differential operators with a singular point, Inverse Problems, 9 (1993), 495–502.
Yurko V. A., On higher-order differential operators with a regular singularity, Mat. Sb. 186 (1995), no.6, 133–160; English transi. in Sbornik; Mathematics 186 (1995), no.6, 901-928.
Levinson N., The inverse Sturm—Liouville problem, Math. Tidsskr. 13 (1949), 25–30.
Leibenzon Z. L., The inverse problem of spectral analysis for higher-order ordinary differential operators, Trudy Moskov. Mat. Obshch. 15 (1966), 70–144; English transl. in Trans. Moscow Math. Soc. 15 (1966).
Bellman R. and Cooke K., Differential-difference equations, Academic Press, New York, 1963.
Borg G., Eine Umkehrung der Sturm—Liouvilleschen Eigenwertaufgabe, Acta Math. 78 (1946), 1–96.
Privalov I. I., Introduction to the theory of functions of a complex variable, 11th ed., Nauka, Moscow, 1967.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1998 Springer Science+Business Media New York
About this chapter
Cite this chapter
Yurko, V. (1998). Sturm—Liouville Differential Operators with Singularities. In: Ramm, A.G. (eds) Spectral and Scattering Theory. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-1552-8_13
Download citation
DOI: https://doi.org/10.1007/978-1-4899-1552-8_13
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4899-1554-2
Online ISBN: 978-1-4899-1552-8
eBook Packages: Springer Book Archive