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Zbl 1179.35334
Mokrani, Houda
Semi-linear sub-elliptic equations on the Heisenberg group with a singular potential. (English)
[J] Commun. Pure Appl. Anal. 8, No. 5, 1619-1636 (2009). ISSN 1534-0392; ISSN 1553-5258/e

Summary: We study the Dirichlet problem for a class of semi-linear sub-elliptic equations on the Heisenberg group with a singular potential. The singularity is controlled by Hardy's inequality, and the nonlinearity is controlled by Sobolev's inequality. We prove the existence of a nontrivial solution for a homogeneous Dirichlet problem.

MSC 2000:: *35R03
35J20 Second order elliptic equations, variational methods
22E30 Analysis on real and complex Lie groups
35J61
35D30

Keywords: Heisenberg group; Hardy's inequality; Sobolev's inequality; singular potential

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