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# Semi-linear sub-elliptic equations on the Heisenberg group with a singular potential

• In this work, 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 homogenous Dirichlet problem.
Mathematics Subject Classification: Primary: 35J20, 22E30; Secondary: 35J60.

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