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In this article, we prove the existence of nontrivial weak solutions to the singular boundary value problem-   Δ    ℍ   n    u  =  μ    g  (  ξ  )  u(  |  z  |   4   +   t  2)    1  2+  λ  f   (  ξ  ,  u  )$-\Delta _{{\mathbb {H}}^{n}} u= \mu \frac{g(\xi ) u}{(|z|^{4}+ t^{2} )^{\frac{1}{2} }} +\lambda f(\xi , u)$    in Ω,u  =  0    $ u =0$    on∂  Ω    $\partial \Omega $    on the Heisenberg group. We employ Bonanno's three critical point theorem to obtain the existence of weak solutions.

Nontrivial solutions for singular semilinear elliptic equations on the Heisenberg group