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.

arXiv admin note: text overlap with arXiv:1705.10100

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• Yamabe-type equations on Carnot groups