A note on existence of antisymmetric solutions for a class of nonlinear Schr?dinger equations

摘要

We consider the nonlinear Schr?dinger equation -Δu + v(x)u=f(u) in ?_N We assume that V is invariant under an orthogonal involution and show the existence of a particular type of sign changing solution. The basic tool employed here is the Concentration-Compactness Principle.