Two Types Of Vector Fields, A Hopf Type And Nonlinear Liouville Type Theorem

In this paper, we give the Hopf type lemma to the generalized Greiner operator and generalized Baouendi-Grushin operator Pa,which are constituted by the vector fields. Then the maximum principles are also obtained. We also prove some Liouville type theorems for two classes of nonlinear degenerate subelliptic equations @Lu + f(,u) = 0and Pau + f( ,u) = 0 on unbounded domains and the whole spaces respectively.