PUB - Publikationen an der Universität Bielefeld

Let M be a complete non-compact Riemannian manifold and let alpha be a Radon measure on M. We study the problem of existence or non-existence of positive solutions to a semilinear elliptic inequality Delta u >= sigma u(q) in M, where q > 1. We obtain necessary and sufficient criteria for existence of positive solutions in terms of Green function of A. In particular, explicit necessary and sufficient conditions are given when M has nonnegative Ricci curvature everywhere in M, or more generally when Green's function satisfies the 3G-inequality. (C) 2019 Elsevier Inc. All rights reserved.