Asymptotic profile for a fourth order PDE with critical exponential growth in dimension four

Abstract

Let Ω be a smooth domain of ℝ4. In this paper, we consider a family (uε)ε>0 of positive solutions in C4(Ω̄) to the equation { Δ 2uε = λuεe 32π2u2ε in Ω uε = ∂u ε/∂n = 0 on ∂Ω where λ ∈ ℝ. Assuming that uε → 0 weakly in H2,02(Ω) while supΩ uε → ∞, we describe the asymptotics of uε as ε → 0.