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arXiv · 1705.10100

Yamabe-type equations on Carnot groups

Giovanni Molica Bisci·Dušan D. Repovš
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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.

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Giovanni Molica Bisci, Dušan D. Repovš. 2017-05-29. Yamabe-type equations on Carnot groups. https://doi.org/10.1007/s11118-016-9587-5

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