A Liouville-type result for quasi-linear elliptic equations on complete Riemannian manifolds

摘要

We extend a Liouville-type result of D. G. Aronson and H. F. Weinberger and E.N. Dancer and Y. Du concerning solutions to the equation Delta(p)u = b(x)f(u) to the case of a class of singular elliptic operators on Riemannian manifolds, which include the phi-Laplacian and are the natural generalization to manifolds of the operators studied by J. Serrin and collaborators in Euclidean setting. In the process, we obtain an a priori lower bound for positive solutions of the equation in consideration, which complements an upper bound previously obtained by the authors in the same context. (C) 2004 Elsevier Inc. All rights reserved.