Inverse eigenvalue problems for a discontinuous Sturm-Liouville operator with two discontinuities

Abstract

In this paper, we consider a discontinuous Sturm-Liouville operator with parameter-dependent boundary conditions and two interior discontinuities. We obtain eigenvalues and eigenfunctions together with their asymptotic approximate formulas. Then, we give some uniqueness theorems by using Weyl function and spectral data, which are called eigenvalues and normalizing constants for solution of inverse problem. MSC: Primary 34A55; secondary 34B24; 34L05

Uniqueness Theorems for Sturm-Liouville Operator with Parameter Dependent Boundary Conditions and Finite Number Of Transmission Conditions

“…For general background of these kind of problems, we refer (e.g.) to the monographs [21][22][23][24][25][26][27].…”