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For a class of sub-elliptic equations on Heisenberg group \(\mathbb{H}^N\) with Hardy type singularity and critical nonlinear growth, we prove the existence of least energy solutions by developing new techniques based on the Nehari constraint. This result extends previous works, e.g., by Han et al. [Hardy-Sobolev type inequalities on the H-type group, Manuscripta Math. 118 (2005), 235–252]

Existence of solution of sub-elliptic equations on the Heisenberg group with critical growth and double singularities