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

Abstract

In this paper we consider the boundary value problem generated on a finite interval by the Sturm-Liouville equation and nonseparated boundary conditions, one of which contains the spectral parameter. We study the main properties of the eigenvalues of the boundary value problem, provide a uniqueness theorem and construct an algorithm for solving the inverse problem by spectral data.

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

“…Little studied are the boundary value problems in the case when the nonseparated boundary conditions depend on the spectral parameter. Only articles [2], [4], [13], [23]- [25], [32]- [34], [40], [41], [45], [47] are devoted to the study of problems of this type. Note that in these papers, for the uniqueness of recovering the unknown coefficients of the differential equation and boundary conditions, at least two spectra of related problems and other additional spectral data are required.…”