Generalized solutions of the Dirichlet problem for the stationary Schrodinger equation on Riemannian manifolds

We study questions of existence of generalized solutions of the Dirichlet problem for the basic models of elliptical equations: the Laplace equation u = 0, and the stationary Schrodinger equations Lu — u−c(x)u = 0, where c(x) is a smooth non-negative function on a non-compact Riemannian manifolds M without boundary. In this arcticle the concept of generalized solutions of the problem is specified and the investigation of guestions of existence Dirichlet problem is affoded to investigation this generalized solution.