Department of Applied Mathematics and Physics, Samara National Research University, Moskovskoye Shosse 34, Samara, 443086; and Department of Mechanics and Mathematics, Saratov State University, Astrakhanskaya 83, Saratov 410012, Russia
In this work, we consider the inverse spectral problem for the impulsive Sturm–Liouville problem on with the Robin boundary conditions and the jump conditions at the point . We prove that the potential on the whole interval and the parameters in the boundary conditions and jump conditions can be determined from a set of eigenvalues for two cases: (i) the potential is given on ; (ii) the potential is given on , where , respectively. It is also shown that the potential and all the parameters can be uniquely recovered by one spectrum and some information on the eigenfunctions at some interior point.
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The authors R. Zhang and C.-F. Yang were supported in part by the National Natural Science Foundation of China (11871031 and 11611530682). The author X.-C. Xu was supported in part by the National Natural Science Foundation of China (11901304).
The author N. P. Bondarenko was supported by Grant 1.1660.2017/4.6 of the Russian Ministry of Education and Science and by Grant 19-01-00102 of the Russian Foundation for Basic Research.
This journal presents original articles on the theory, numerics and applications of inverse and ill-posed problems. These inverse and ill-posed problems arise in mathematical physics and mathematical analysis, geophysics, acoustics, electrodynamics, tomography, medicine, ecology, financial mathematics etc. Articles on the construction and justification of new numerical algorithms of inverse problem solutions are also published.