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)?mu+f(u)=0,x??N,N?m>1, where ?mu=?;{dot operator}(|?;u|m-2?;u). Our result is new even for the case of the Laplacian (m=2). © 2013 Elsevier Inc.