Nontrivial solutions for singular semilinear elliptic equations on the Heisenberg group

Abstract

Abstract. 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.