Semi-classical limit for radial non-linear Schrodinger equation

Abstract

We consider the nonlinear Schrodinger equation

epsilon(2)Delta u - V (x) u + | u|(p-1) u = 0, x is an element of R-N,

with superlinear and subcritical nonlinearity. Assuming that the potential is radially symmetric we find radial sign-changing solutions of the equation that concentrate in a ball, as the parameter e goes to zero. We study the asymptotic profile of these highly oscillatory solutions, completely characterizing their behavior by means of an envelope function.