Positive Solutions of Yamabe Type Equations on Complete Manifolds and Applications

We study the semilinear equationΔu+a(x) u=b(x) uσ(σ>1) on a complete Riemannian manifold. We determine conditions on the coefficients that guarantee existence and nonexistence of positive solutions. A very general uniqueness result is also established. Our main results are valid without explicit curvature assumptions, and appear to be new even in Rm.