Geodesic
On main equation for inverse Sturm--Liouville operator with discontinuous coefficient
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential Equations and Mathematical Physics, Tome 225 (2023), pp. 73-86.

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In this work, a boundary-value problem for the Sturm–Liouville operator with discontinuous coefficient is examined. The main equation for the inverse problem for the boundary-value problem is obtained and the uniqueness of its solution is proved.
Mots-clés : main equation
Keywords: discontinuous Sturm–Liouville operator, inverse problem. 
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     title = {On main equation for inverse {Sturm--Liouville} operator with discontinuous coefficient},
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D. Karahan; Kh. R. Mamedov; I. F. Hashimoglu. On main equation for inverse Sturm--Liouville operator with discontinuous coefficient. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential Equations and Mathematical Physics, Tome 225 (2023), pp. 73-86. http://geodesic.mathdoc.fr/item/INTO_2023_225_a6/

[1] Akhtyamov A. M., Teoriya identifikatsii kraevykh uslovii i ee prilozheniya, Fizmatlit, M., 2009

[2] Levitan B. M., Obratnye zadachi Shturma—Liuvillya, Nauka, M., 1984 | MR

[3] Levitan B. M., Gasymov M. G., “Opredelenie differentsialnogo uravneniya po dvum spektram”, Usp. mat. nauk., 19:2 (116) (1964), 3–63 | MR | Zbl

[4] Levitan B. M., Sargsyan I. S., Operatory Shturma—Liuvillya i Diraka, Nauka, M., 1988 | MR

[5] Lyusternik L. A., Sobolev V. I., Elementy funktsionalnogo analiza, Nauka, M., 1965 | MR

[6] Marchenko V. A., Spektralnaya teoriya operatorov Shturma—Liuvillya, Naukova dumka, Kiev, 1972

[7] Rasulov M. L., Metod konturnogo integrala, Nauka, M., 1964

[8] Tikhonov A.N., Samarskii A.A., Uravneniya matematicheskoi fiziki, Nauka, M., 1977 | MR

[9] Yurko V. A., Obratnye spektralnye zadachi i ikh prilozheniya, Izd-vo Sarat. ped. in-ta, Saratov, 2001

[10] Akhmedova E. N., “On representation of solution of Sturm–Liouville equation with discontinuous coefficients”, Proc. Inst. Math. Mech. Natl. Acad. Sci. Azerbaijan., 16:24 (2002), 5–9 | MR | Zbl

[11] Akhmedova E. N., Huseynov H. M., “The main equation of the inverse Sturm–Liouville problem with discontinuous coefficients”, Proc. Inst. Math. Mech. Natl. Acad. Sci. Azerbaijan., 26:34 (2007), 17–32 | MR | Zbl

[12] Akhtyamov A. M., Mouftakhov A. V., “Identification of boundary conditions using natural frequencies”, Inv. Probl. Sci. Eng., 12:4 (2004), 393–408 | DOI | MR

[13] Aliev B. A., Yakubov Ya. S., “Solvability of boundary value problems for second-order elliptic differential-operator equations with a spectral parameter and with a discontinuous coefficient at the highest derivative”, Differ. Equat., 50:4 (2014), 464–475 | DOI | MR | Zbl

[14] Altinisik N., Kadakal M., Mukhtarov O., “Eigenvalues and eigenfunctions of discontinuous Sturm–Liouville problems with eigenparameter dependent boundary conditions”, Acta Math. Hung., 102:1-2 (2004), 159–175 | DOI | MR | Zbl

[15] Anderssen R. S., “The effect of discontinuities in destiny and shear velocity on the asymptotic overtone structure of torsional eigenfrequencies of the Earth”, Geophys. J. R. Astr. Soc., 50 (1977), 303–309 | DOI

[16] Borg G., “Eine Umkehrung der Sturm–Liouvilleschen Eigenwertaufgabe”, Acta Math., 78 (1946), 1–96 | DOI | MR | Zbl

[17] Carlson R., “An inverse spectral problem for Sturm–Liouville operators with discontinuous coefficients”, Proc. Am. Math. Soc., 120:2 (1994), 5–9 | DOI | MR

[18] Freiling G., Yurko V., Inverse Sturm–Liouville problems and Their Applications, Nova Science Publ., 2008 | MR

[19] Hald O. H., “Discontinuous inverse eigenvalue problems”, Commun. Pure Appl. Math., 37 (1984), 539–577 | DOI | MR | Zbl

[20] Hao D. N., Methods for Inverse Heat Conduction Problems, Peter Lang Verlag, Frankfurt/Main etc., 1998 | MR | Zbl

[21] Karahan D., Mamedov Kh. R., “Uniqueness of the solution of the inverse problem for one class of Sturm–Liouville operator”, Proc. Inst. Math. Mech. Natl. Acad. Sci. Azerbaijan., 40 (2014), 233–244 | MR | Zbl

[22] Marchenko V. A., Strum–Liouville Operators and Their Aplications, Birkhäuser Verlag, Basel–Boston–Stuttgart, 1986 | MR

[23] Nabiev A. A., Amirov R. K., “On the boundary value problem for the Sturm–Liouville equation with the discontinuous coefficient”, Math. Meth. Appl. Sci., 36:13 (2013), 1685–1700 | DOI | MR | Zbl

[24] Poschel J., Trubowitz E., Inverse Spectral Theory, Academic Press, New York, 1987 | MR | Zbl

[25] Sedipkov A. A., “The inverse spectral problem for the Sturm–Liouville operator with discontinuous potential”, J. Inv. Ill-Posed Probl., 20 (2012), 139–167 | DOI | MR | Zbl