Incomplete and Interior Inverse Problem for a Discontinuous Differential Pencil with the Spectral Boundary Condition on the Half-Line

Differential pencils on the half-line with a spectral boundary condition having a discontinuity in an interior point are investigated. We prove two uniqueness theorems: (i) knowing β1 ,β0 and potentials p,q on (0,a), only eigenvalues suffice to determine the boundary value problem B. (ii) some in formation on eigenfunctions at x = a and eigenvalues establish the boundary value problem B.