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Semi-linear sub-elliptic equations on the Heisenberg group with a singular potential. (English) Zbl 1179.35334

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:

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
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