  The work is devoted to the study of Laplace operator when the potential is a
singular generalized function and plays the role of a singular perturbation of
a Laplace operator. Abstract theorem obtained earlier by the authors B.N.
Biyarov and G.K. Abdrasheva applies to this. The main purpose of the study is
the spectral issue. Singular perturbations for differential operators have been
studied by many authors for the mathematical substantiation of solvable models
of quantum mechanics, atomic physics, and solid state physics. In all these
cases, the problems were self-adjoint. In this paper, we consider
non-self-adjoint singular perturbation problems. A new method has been
developed that allows investigating the considered problems.
