Asymptotic behavior of a fourth order mean field equation with Dirichlet boundary condition
Frédéric Robert, Juncheng Wei · Indiana University Mathematics Journal · 2008
Abstract. We consider asymptotic behavior of the following fourth order equation ∆ 2 e u = ρ u R Ω eu in Ω, u = ∂νu = 0 on ∂Ω dx where Ω is a smooth oriented bounded domain in R4. Assuming that 0 < ρ ≤ C, we completely characterize the asymptotic behavior of the unbounded solutions. 1.