On Spectrum of Schrödinger Operator on Manifold of a Special Type

The main subject of the paper is spectrum of the Schrödinger operator on weighted quasimodel manifold with an end, which is warped product of a special type. We prove the criterion of discreteness for the spectrum of the operator in terms of metric coefficients and potential of the operator. As the conclusion we made some remarks on the corollaries of the proved theorem and on its extension to more complex quasimodel manifolds.