An inverse problem by eigenvalues of four spectra

Certain parts of the Dirichlet–Dirichlet, Neumann–Dirichlet, Dirichlet–Neumann and Neumann–Neumann spectra are used to find the potential of the Sturm–Liouville equation on a finite interval. This problem possesses a unique solution. Conditions are found necessary and sufficient for four sequences to be the corresponding parts of the four spectra.