Yamabe-Type Equations on Carnot Groups

This article is concerned with a class of elliptic equations on Carnot groups depending of one real positive parameter and involving a critical nonlinearity. As a special case of our results we prove the existence of at least one nontrivial solution for a subelliptic critical equation defined on a smooth and bounded domain D of the Heisenberg group H-n = C-n x R. Our approach is based on pure variational methods and locally sequentially weakly lower semicontinuous arguments.