Abstract
Let M be a complete non-compact Riemannian manifold and let σ be a Radon measure on M. We study the problem of existence or non-existence of positive solutions to a semilinear elliptic inequality−Δu≥σuqinM, where q>1. We obtain necessary and sufficient criteria for existence of positive solutions in terms of Green function of Δ. 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.
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