  We establish the existence of multiple sign-changing solutions to the
quasilinear critical problem $$-\Delta_{p} u=|u|^{p^*-2}u, \qquad u\in
D^{1,p}(\mathbb{R}^{N}),$$ for $N\geq4$, where
$\Delta_{p}u:=\mathrm{div}(|\nabla u|^{p-2}\nabla u)$ is the $p$-Laplace
operator, $1<p<N$ and $p^*:=\frac{Np}{N-p}$ is the critical Sobolev exponent
