On the asymptotic behavior of solutions of the stationary Schrodinger equation on non-compact Riemannian manifolds

We study the problem of asymptotic behavior and belonging to given functional class of solutions of the Schro¨dinger equation on a noncompactRiemannian manifold without boundary. In the present work we suggest concept of equivalence in the classes of continuous functions on a non-compact Riemannian manifold with respect to certain norms in this spaces. Also we establish the interrelation between problems of existence of solutions of the Schro¨dinger equation on and off some compact in a given class of equivalent functions. We study questions of existence and belonging to given functional class of solutions of the Schro¨dinger equation𝐿𝑢 ≡ Δ𝑢 - 𝑐(𝑥)𝑢 = 0, (1)⊂∈ ≥where 𝑐(𝑥) 𝐶0,α(Ω), 𝑐(𝑥) 0, 0