The asymptotic behaviour of the ground state solutions for Hénon equation

The main purpose of this paper is to analyze the asymptotic behaviour of the ground state solution of Hénon equation −Δu = |x|αup−1 in Ω, u = 0 on ∂Ω (Ω ⊂ Rn is a ball centered at the origin). It proved that for p close to 2∗ = 2n/(n − 2) (n 3), the ground state solution up has a unique maximum point xp and dist(xp, ∂Ω)→0 as p→2∗. The asymptotic behaviour of up is also given, which deduces that the ground state solution is non-radial.  2003 Elsevier Science (USA). All rights reserved