On capacitary characteristics of noncompact Riemannian manifolds

In this paper we introduce the concept of $L$-massive subsets of non-compact Riemannian manifolds, also their properties are studied. It is proved that non-trivial bounded solution of considered equation exists on non-compact Riemannian manifold if and only if there is $L$-massive set on it. Also proved similar statement for solutions of semilinear equations with finite energy integral.