Extending the previous work on the corresponding inverse Dirichlet problem, we present a factorization method for the solution of an inverse Neumann boundary value problem for harmonic vector fields. 2000 Mathematics Subject Classification: 31B10, 31B20, 45A05, 45Q05, 78A30.

this paper is devoted to the proof of the unique solvability ofthe inverse problems for second-order differential operators withregular singularities. it is shown that the potential functioncan be determined from spectral data, also we prove a uniquenesstheorem in the inverse problem.