Asymptotic behavior of least energy solutions for a biharmonic problem with nearly critical growth

Abstract

We study the asymptotic behavior of least energy solutions to the equation Δ²u=c₀K(x)u^p_ε with the Navier boundary condition as ε→+0, where Ω is a smooth bounded domain in R^N (N≥5), c₀=(N−4)(N−2)N(N+2) and p_ε=(N+4)/(N−4)−ε, ε>0. Under some assumptions on the coefficient function K, we obtain fairly precise asymptotics of the L^∞-norm of least energy solutions.