“A priori” estimates, uniqueness and existence of positive solutions of Yamabe type equations on complete manifolds

We study the asymptotic behaviour of non-negative solutions of Yamabe type equations on a complete Riemannian manifold. Then we provide a comparison result, based on a form of the weak maximum principle at infinity, which together with the “a priori” estimates previously obtained, yields uniqueness under very general Ricci assumptions. The paper ends with an existence result and an application to the non-compact Yamabe problem. © 2006 Elsevier Inc. All rights reserved