The asymptotic behaviour of the ground state solutions for Henon equation

The main purpose of this paper is to analyze the asymptotic behaviour of the ground state solution of xenon equation -Deltau = \x\(alpha)u(p-1) in Omega, u = 0 on partial derivativeOmega (Omega subset of R-n is a ball centered at the origin). It proved that for p close to 2* = 2n/(n - 2) (n greater than or equal to 3), the ground state solution u(p) has a unique maximum point x(p) and dist(x(p), partial derivativeOmega) --> 0 as p --> 2*. The asymptotic behaviour of u(p) is also given, which deduces that the ground state solution is non-radial. (C) 2003 Elsevier Science (USA). All rights reserved.