Abstract

In this article we study standing wave solutions for the nonlinear Schrödinger equation, which correspond to solutions of the equation ?2u? - V(x)u + u|u|p-1 = 0, x ? ?. We are interested in solutions having a prescribed L2 norm, exhibiting high oscillatory behavior and concentrating in an interval. We prove existence of such solutions and we study their asymptotic behavior as the parameter ? goes to zero. In particular we obtain an envelope function describing the amplitude of the solutions and we identify their asymptotic density.