Inverse eigenvalue problems for Sturm–Liouville equations with spectral parameter linearly contained in one of the boundary conditions

Abstract

Abstract. Inverse problems of recovering the coefficients of Sturm-Liouville problems with the eigenvalue parameter linearly contained in one of the boundary conditions are studied: 1) from the sequences of eigenvalues and norming constants; 2) from two spectra.Necessary and sufficient conditions for the solvability of these inverse problems are obtained.

Recovering singular Sturm-Liouville differential pencils from spectral data

“…Denote δ,R := δ ∩ {μ : |μ| ≤ R}. Contracting the contour in (21) to the real axis and using (15) and (16), we get…”

“…Inverse problems for differential operators with boundary conditions dependent on the spectral parameter are more difficult to investigate, and nowadays there are only a number of papers in this direction (see [11][12][13][14][15][16][17]). In particular, [11][12][13][14][15][16] study such problems on a finite interval. Inverse spectral problems for the non-self-adjoint Sturm-Liouville pencil (1) and (2) on the half-line were considered in [17], where recovering L from the Weyl function was studied.…”

An inverse nodal problem for p-Laplacian Sturm-Liouville equation with Coulomb potential

“…For instance, Sturm-Liouville equation including spectral parameter in boundary conditions arises in heat and one-dimensional wave equation by seperation of variables. There are many studies on these type problems in the literature (see [7,13,14,27,29,32,33]). …”

Inverse Problems for Dirac Operator with Boundary Conditions İnvolving A Herglotz-Nevanlinna function

“…In 1977, Fulton [13] also examined the Sturm-Liouville eigenvalue problem. Inverse problems for some classes of differential operators linearly eigenvalue dependent are analysed in diverse papers (see [1,2,9,17,22]). More general boundary conditions are observed in [4-6, 10, 12, 26, 29, 30, 34,35].…”