Inverse Sturm-Liouville problems with two supplementary discontinuous conditions on two symmetric disjoint intervals

چکیده مقاله

In this paper‎, ‎we consider Sturm-Liouville problems on two symmetric disjoint intervals with two supplementary discontinuous conditions at an interior point‎. ‎First‎, ‎we investigate some spectral properties of boundary value problems‎, ‎and obtain the asymptotic form of the eigenvalues and the eigenfunctions‎. ‎Then‎, ‎the eigenfunction expansion of Green's function is presented and we prove the uniqueness theorems for the solution of the inverse problem‎, ‎and reconstruct the Sturm-Liouville operator and the coefficients of boundary conditions using the Weyl $m$-function and spectral data‎. ‎Also‎, ‎numerical examples are presented‎