We consider the boundary value problem Δu + |x|2α |u|p-1u = 0, -1 < α ≠ 0, in the unit ball B with the homogeneous Dirichlet boundary condition, when p is a large exponent. By a constructive way, we prove that for any positive integer m, there exists a multi-peak nodal solution up whose maxima and minima are located alternately near the origin and the other m points = (λcos(2π(l-1)/m), λ sin(2π(l-1)/m), l = 2, … ,m+ 1, such that as p goes to +∞,
p|x|2α|μp|p-1μp→8πe(1 + α)δ0 +, where λ ∈ (0, 1), m is an odd number with (1+α)(m+2)-1 > 0, or m is an even number. The same techniques lead also to a more general result on general domains.