On the discrete spectrum of non-self-adjoint Schrodinger differential equation with an operator coefficient

We study the discrete part of spectrum of a singular non-self-adjoint second-order differential equation on a semiaxis with an operator coefficient. Its boundedness is proved. The result is applied to the Schrodinger boundary value problem -Deltau+q(x)u=lambda(2)u, u\(partial derivativeD)=0, with a complex potential q(x) in an angular domain. (C) 2004 American Institute of Physics.