The inverse spectral problem for pencils of differential operators

Reconstruction of energy-dependent Sturm-Liouville equations from two spectra. II

“…The inverse spectral problems for (1) with p ∈ W 1 2 (0, 1) and q ∈ L 2 (0, 1) and with Robin boundary conditions were discussed by M. Gasymov and G. Guseinov in their short paper [3] of 1981 containing no proofs. Such problems were also considered in [2,4,13,14,22], but only Borg-type uniqueness results were obtained therein.…”

Inverse spectral problems for energy-dependent Sturm–Liouville equations

“…Then λ 2 is related to the energy of the system, thus 1 2 (0, 1) and q ∈ L 2 (0, 1) and with Robin boundary conditions was discussed by M. Gasymov and G. Guseinov in their short paper [10] of 1981 containing no proofs. Such problems for (quasi)-periodic boundary conditions were considered in, e.g., [12,13,37,38,55]; however, typically only Borg-type uniqueness results were established therein. Some nonclassical settings of the inverse spectral problem (e.g., those with mixed given data, Hochstadt-type problems, or inverse nodal problems) were discussed in [26][27][28].…”

An inverse nodal problem for differential pencils with complex spectral parameter dependent boundary conditions

“…Some aspects of this type problems were studied by many authors (see [25], [26], [27], [28], [29], [30], [31], [32], [33], [34], [35], [36], [37], [38]). Such problems play an important role in mathematics and have many applications in natural sciences and engineering.…”