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. 
@article{MZM_2018_103_1_a5,
     author = {Ying Yang and Guangsheng Wei},
     title = {Inverse {Scattering} {Problems} for {Sturm--Liouville} {Operators} with {Spectral} {Parameter} {Dependent} on {Boundary} {Conditions}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {65--74},
     publisher = {mathdoc},
     volume = {103},
     number = {1},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2018_103_1_a5/}
}
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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/