QUASILINEAR EQUATIONS WITH SOURCE TERMS ON CARNOT GROUPS.

In this paper we give necessary and sufficient conditions for the existence of solutions to quasilinear equations of Lane-Emden type with measure data on a Carnot group G of arbitrary step. The quasilinear part involves operators of the p-Laplacian type ?_{G, p}, 1 < p < 8. These results are based on new a priori estimates of solutions in terms of nonlinear potentials of Th. Wolff's type. As a consequence, we characterize completely removable singularities, and we prove a Liouville type theorem for supersolutions of quasilinear equations with source terms which has been known only for equations involving the sub-Laplacian (p = 2) on the Heisenberg group. [ABSTRACT FROM AUTHOR]