Localized nodal solutions for a critical nonlinear Schrödinger equation

Abstract

For semiclassical nonlinear Schrödinger equations with Sobolev critical exponent we propose and implement a procedure to construct an unbounded sequence of semiclassical bound states which are localized nodal solutions and are concentrated at a local minimum set of the potential. Our approach does not need any non-degeneracy condition of the limiting equation and is robust for more general problems.