Abstract:
The goal of this paper is to establish singular Adams type inequality for biharmonic operator on Heisenberg group. As an application, we establish the existence of a solution to
Δ2Hnu=f(ξ,u)ρ(ξ)a in Ω,u|∂Ω=0=∂u∂ν∣∣∣∂Ω,
ΔHn2u=f(ξ,u)ρ(ξ)a in Ω,u|∂Ω=0=∂u∂ν|∂Ω,
where 0∈Ω⊆H40∈Ω⊆H4 is a bounded domain, 0≤a≤Q,(Q=10).0≤a≤Q,(Q=10). The special feature of this problem is that it contains an exponential nonlinearity and singular potential.