Asymptotic behaviour of ground state solutions for the Henon equation

Let B-1(0) subset of R-N be the unit ball centred at the origin, N >= 3. In this paper, we analyse the profile of the ground state solution of the Henon equation - Delta u = |x|(alpha)u(p-1) in B-1(0), u = 0 on partial derivative B-1(0). We prove that for fixed p is an element of (2, 2(*)), (2(*) = 2N/(N - 2)), the maximum point x(alpha) of the ground state solution u(alpha) satisfies alpha(1 - vertical bar x(alpha)vertical bar) -> l is an element of (0, +infinity) as alpha -> infinity. We also obtain the asymptotic behaviour of u(alpha), which shows that the ground state solution is non-radial. Moreover, we prove the existence of multi-peaked solutions and give their asymptotic behaviour.