Bounded solutions of the stationary Schrodinger equation with finite energy integral on model manifolds

Conditions for the existence of nontrivial bounded solutions of the stationary Schrodinger equation with a nite energy integral on model varieties are obtained. A condition for the existence of nontrivial bounded solutions with a nite integral of energy in the exterior of a compactum on arbitrary Riemannian manifolds is also obtained. Let D = (0; + ) S, where S is compact Riemannian manifold. Metrics on D is followingds2 = dr2 + g2(r)dθ2.∞Where g(r) is positive, smooth on (0, + ) function, dθ2 is metrics on S. We will study solutions of the stationary Schrodinger equationΔu - c(r)u = 0 on D. Let r0 = const > 0,n = dim D.Theorem 1.If one of the following conditions is ful lled on D:∞μ) R