Nontrivial solutions for singular semilinear elliptic equations on the Heisenberg group

Abstract

In this article, we prove the existence of nontrivial weak solutions to the singular boundary value problem -Δℍnu=μg(ξ)u(|z|4+t2)12+λf(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.

Keywords

• singular elliptic equations
• variational methods
• nontrivial solutions
• 35j20
• 35j75