Title: Nonlinear elliptic equations on Carnot groups,
Abstract: This article concerns a class of elliptic equations on Carnot groups
depending on one real positive parameter and involving a subcritical
nonlinearity (for the critical case we refer to G. Molica Bisci and D.
Repovš, Yamabe-type equations on Carnot groups, Potential Anal. 46:2
(2017), 369-383; arXiv:1705.10100 [math.AP]). As a special case of our results
we prove the existence of at least one nontrivial solution for a subelliptic
equation defined on a smooth and bounded domain $D$ of the Heisenberg group
$\mathbb{H}^n=\mathbb{C}^n\times \mathbb{R}$. The main approach is based on
variational methods.