  We prove the existence of one positive, one negative, and one sign-changing
solution of a $p$-Laplacian equation on $\mathbb{R}^N$, with a $p$-superlinear
subcritical term. Sign-changing solutions of quasilinear elliptic equations set
on the whole of $\mathbb{R}^N$ have only been scarcely investigated in the
literature. Our assumptions here are similar to those previously used by some
authors in bounded domains, and our proof uses fairly elementary critical point
theory, based on constraint minimization on the nodal Nehari set. The lack of
compactness due to the unbounded domain is overcome by working in a suitable
weighted Sobolev space.
