LAUSR

Abstract In this paper we investigate a semi-linear degenerate elliptic equation Δ L u + h ( ξ ) u p + g ( ξ ) u q = 0 related to the generalized Baouendi-Grushin vector fields, where p and q satisfy certain conditions. The idea is to extend the Obata method applying elliptic equations to the degenerate elliptic equation. In consideration of noncommutative relations of the generalized Baouendi-Grushin vector fields, an identity corresponding to the degenerate elliptic equation is established. By using a special truncated function, the identity deformation and accurate estimates, we derive Liouville theorems which show that all nonnegative solutions to the equation are trivial.