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)Δmu+f(u)=0,x∈RN,N⩾m>1, where Δmu=∇⋅(|∇u|m−2∇u)Δmu=∇⋅(|∇u|m−2∇u). Our result is new even for the case of the Laplacian (m=2m=2).