Boundary value problems for second-order differential equations on a finite inerval having a discontinuity in an interior point are studied. Completeness and expansion theorems are obtained and inverse problems are inverstigataed. For three classes of inverse problems the uniqueness theorems are proved. Necessary and sufficient conditions along with a procedure for the solution of the inverse problems are given.

Inverse problems of spectral analysis are studied for Sturm–Liouville differential operators on arbitrary compact graphs. The uniqueness of recovering operators from their spectra is proved, and a constructive procedure for the solution of this class of inverse problems is provided.