Abstract :
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
