On Capacitary Characteristics of Noncompact Riemannian Manifolds

We introduce the notion of an L-massive subset in a noncompact Riemannian manifold and study properties of such subsets. It is proved that a semilinear elliptic equation on a noncompact Riemannian manifold has a nontrivial bounded solution if and only if there exists an L-massive subset in this manifold. A similar assertion is also proved for solutions of semilinear equations with finite energy integral.