Yamabe-type equations on Carnot groups

Abstract

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} ${\mathbb{H}}^n={\mathbb{C}}^n\times \mathbb{R}$. Our approach is based on pure variational methods and locally sequentially weakly lower semicontinuous arguments.

References in corpus (1)

• Nonlinear elliptic equations on Carnot groups