Multiple solutions of quasilinear elliptic equations in \(\mathbb R^N\) (Q606251)

Summary: Assume that \(Q\) is a positive continuous function in \(\mathbb R^N\) and satisfies some suitable conditions. We prove that the quasilinear elliptic equation \(-\Delta_pu+|u|^{p-2}u=Q(z)|u|^{q-2}u\) in \(\mathbb R^N\) admits at least two solutions in \(\mathbb R^N\) (one is a positive ground-state solution and the other is a sign-changing solution).