Existence and multiplicity results for a fourth order mean field equation

In this article we consider the following fourth order mean field equation on smooth domain Ω⋐R4Ω⋐R4:Δ2u=ϱKeu∫ΩKeuin Ω,u=Δu=0on ∂Ω, where ϱ∈Rϱ∈R and 0