On the Well-possedness of the Problem of Reconstruction of Non-separate   Boundary Conditions
  We consider an inverse spectral problem with the third-order differential equation and the non-separated boundary conditions. Two theorems on the uniqueness of the solution of this problem are proved, and a method for establishing the unknown conditions is obtained, using 19 eigenvalues. The method of approximate calculation of unknown boundary conditions is explained, with the help of an example. 
A. M. Akhtyamov, A. V. Mouftakhov, M. Teicher, L. S. Yamilova