Geodesic
Inverse Scattering Problems for Sturm--Liouville Operators with Spectral Parameter Dependent on Boundary Conditions
Matematičeskie zametki, Tome 103 (2018) no. 1, pp. 65-74.

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In this paper, we consider the inverse scattering problem for the Sturm–Liouville operator on the half-line $[0,\infty)$ with Herglotz function of spectral parameter in the boundary condition. The scattering data of the problem is defined, and its properties are investigated. The main equation is obtained for the solution of the inverse problem and it is shown that the potential is uniquely recovered in terms of the scattering data.
Keywords: Sturm–Liouville operator, inverse problem, scattering data, spectral parameter. 
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Ying Yang; Guangsheng Wei. Inverse Scattering Problems for Sturm--Liouville Operators with Spectral Parameter Dependent on Boundary Conditions. Matematičeskie zametki, Tome 103 (2018) no. 1, pp. 65-74. http://geodesic.mathdoc.fr/item/MZM_2018_103_1_a5/

[1] P. Deift, E. Trubowitz, “Inverse scattering on the line”, Comm. Pure Appl. Math., 32:2 (1979), 121–251 | DOI | MR | Zbl

[2] B. M. Levitan, Inverse Sturm–Liouville Problems, VNU Science Press, Utrecht, 1987 | MR | Zbl

[3] T. Aktosun, R. Weder, “Inverse spectral-scattering problem with two sets of discrete spectra for the radial Schrödinger equation”, Inverse Problems, 22:1 (2004), 89–114 | DOI | MR | Zbl

[4] T. Aktosun, “Construction of the half-line potential from the Jost function”, Inverse Problems, 20:3 (2004), 859–876 | DOI | MR | Zbl

[5] V. A. Marchenko, Sturm–Liouville Operator and Applications, Birkhäuser Verlag, Basel, 1986 | MR | Zbl

[6] G. Wei, H. K. Xu, “On the missing bound state data of inverse spectral-scattering problems on the half-line”, Inverse Probl. Imaging, 9:1 (2015), 239–255 | DOI | MR | Zbl

[7] A. Çöl, “Inverse spectral problem for Sturm–Liouville operator with discontinuous coefficient and cubic polynomials of spectral parameter in boundary condition”, Adv. Difference Equ., 2015 (2015), 132 | DOI | MR

[8] Kh. R. Mamedov, “Edinstvennost resheniya obratnoi zadachi teorii rasseyaniya dlya operatora Shturma–Liuvillya so spektralnym parametrom v granichnom uslovii”, Matem. zametki, 74:1 (2003), 142–146 | DOI | MR | Zbl

[9] Kh. R. Mamedov, “On the inverse problem for Sturm–Liouville operator with a nonlinear spectral in the boundary condition”, J. Korean Math. Soc., 46:6 (2009), 1243–1254 | DOI | MR | Zbl

[10] E. A. Pocheikina-Fedotova, “Ob obratnoi kraevoi zadache na poluosi dlya differentsialnogo uravneniya 2-go poryadka”, Izv. vuzov. Matem., 1972, no. 7, 75–84 | MR | Zbl

[11] V. A. Yurko, “Obratnaya zadacha dlya puchkov differentsialnykh operatorov”, Matem. sb., 191:10 (2000), 137–160 | DOI | MR | Zbl

[12] V. A. Yurko, “O vosstanovlenii puchkov differentsialnykh operatorov na poluosi”, Matem. zametki, 67:2 (2000), 316–320 | DOI | MR | Zbl

[13] C. T. Fulton, S. Pruess, “Numerical methods for a singular eigenvalue problem with eigenparameter in the boundary conditions”, J. Math. Anal. Appl., 71:2 (1979), 431–462 | DOI | MR | Zbl

[14] B. Ja. Levin, Distribution of Zeros of Entire Functions, Amer. Math. Soc., Providence, RI, 1980 | MR | Zbl

[15] F. Gesztesy, B. Simon, “On the determination of a potential from three spectra”, Differential Operators and Spectral Theory, Amer. Math. Soc. Transl. Ser. 2, 189, Amer. Math. Soc., Providence, RI, 1999, 85–92 | MR | Zbl