On the existence of sign changing bound state solutions of a quasilinear equation

In this paper we establish the existence of bound state solutions having a prescribed number of sign changes for (P) Δ_mu+f(u)=0, x∈R^N, N⩾m>1, where Δ_mu=∇ṡ(|∇u). Our result is new even for the case of the Laplacian (m=2).