A note on existence of antisymmetric solutions for a class of nonlinear Schrödinger equations

Abstract

We consider the nonlinear Schrödinger equation $$-\triangle u + V(x)u= f(u)\quad {\rm in}\quad \mathbb{R}^N.$$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.