Abstract :
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 pu = b(x)f (u) to the case of a class of
singular elliptic operators on Riemannian manifolds, which include the -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
