Mokrani, Houda Semi-linear sub-elliptic equations on the Heisenberg group with a singular potential. (English) Zbl 1179.35334 Commun. Pure Appl. Anal. 8, No. 5, 1619-1636 (2009). 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. Cited in 20 Documents MSC: 35R03 PDEs on Heisenberg groups, Lie groups, Carnot groups, etc. 35J20 Variational methods for second-order elliptic equations 22E30 Analysis on real and complex Lie groups 35J61 Semilinear elliptic equations 35D30 Weak solutions to PDEs Keywords:Heisenberg group; Hardy’s inequality; Sobolev’s inequality; singular potential PDFBibTeX XMLCite \textit{H. Mokrani}, Commun. Pure Appl. Anal. 8, No. 5, 1619--1636 (2009; Zbl 1179.35334) Full Text: DOI