Existence of Many Nonradial Positive Solutions of the Hénon Equation in R³

Let $B_1$ be the open unit ball in $\mathbb{R}^3$ and let $2<p<6$. We show that for each $m\in \mathbb{N}$, there exists $\alpha_0>0$ such that for each $\alpha\geq \alpha_0$, there exist at least $m$ nonradial positive solutions of $$-\Delta u = |x|^\alpha |u(x)|^{p-2}u(x) \quad\text{in $B_1$,}\qquad u = 0 \quad\text{on $\partial B_1$,}$$ which are mutually nonequivalent if $m\geq 2$.