On solvability of three spectra problem

Three spectral problems generated by the same Sturm-Liouville equation are considered: Neumann-Dirichlet problem (the Neumann condition at the left end and the Dirichlet condition at the right end) on the whole interval [0, a], Neumann-Dirichlet problem on [0,a/2] and Dirichlet-Dirichlet problem on [a/2,a]. The three spectra inverse problem, i.e. the problem of recovering the Sturm-Liuville equation using the three spectra of these boundary value problems is completely solved.