Bounded solutions of the stationary Shr"odinger equation on the model manifolds

In this paper we consider solutions of the stationary Shrodinger equation on the non-compact Riemannian manifolds which is the generalized spherically symmetric manifolds. By the spectral properties of such manifolds the exact estimations of the dimension of the space of bounded and the cone of non-negative solutions of the stationary Shrödinger equation were obtained.