Reconstruction of the diffusion equation with singular coefficients for two spectra

Inverse spectral and inverse nodal problems for Sturm-Liouville equations with point $\delta$ and $\delta'$-interactions

“…BVPs with discontinuities in an interior point also appear in geophysical models for oscillations of the Earth (see [10]). Discontinuous inverse problems (in various formulations) have been considered in [4], [5], [6], [9], [18], [20], [22]. In the present paper we obtain some results on inverse spectral and inverse nodal problems and establish connections between them.…”

Solvability of the inverse spectral problem for Sturm-Liouville operator with spectral parameter in the boundary condition

“…Such problems also arise in technical physics, mechanics, acoustics of flow channels, electrodynamics, and other areas [11], [36], [49]. In the case of separated boundary conditions, some variants of such problems are completely solved (see [5]- [7], [9], [10], [15]- [18], [22], [28], [42], [50]). Little studied are the boundary value problems in the case when the nonseparated boundary conditions depend on the spectral parameter.…”

Spectral properties of the Sturm-Liouville operator with a spectral parameter quadratically included in the boundary condition

“…The characteristics of the spectrum of Sturm-Liouville operators in the case of regular, irregular and degenerate boundary conditions were given in the papers [19]- [21 ], in the case of boundary conditions containing a spectral parameter in [6]. Inverse problems on a whole axis, semi-axis and section for Sturm-Liouville operators with a spectral parameter in the discontinuity condition were solved in [8], [9], [12]. Note that in the general case of boundary conditions, a uniqueness problem of the reconstruction of a differential equation and boundary conditions was studied in the papers [30], [32], [35] by different methods.…”