Boundary value problems on hedgehog-type graphs for Sturm-Liouville differential operators with general matching conditions are studied. We investigate inverse spectral problems of recovering the coefficients of the differential equation from the spectral data. For this inverse problem we prove a uniqueness theorem and provide a procedure for constructing its solution.

An inverse spectral problem is studied for the non-selfadjoint matrix Sturm-Liouville differential equation on the half-line. We give a formulation of the inverse problem, prove the corresponding uniqueness theorem and provide a constructive procedure for the solution of the inverse problem by the method of spectral mappings. The obtained results are natural generalizations of the classical results in inverse problem theory for scalar Sturm-Liouville operators.

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Inverse nodal and inverse spectral problems are studied for second-order differential operators on a finite interval with discontinuity conditions inside the interval. Uniqueness theorems are proved, and a constructive procedure for the solution is provided.