Thick clusters for the radially symmetric nonlinear Schrodinger equation

This article is devoted to the study of radially symmetric solutions to the nonlinear Schrodinger equation epsilon(2) Delta u - V (r)u + vertical bar u vertical bar(p-1) u = 0 in B, partial derivative u/partial derivative n = 0 on partial derivative B, where B is a ball in R-N, 1 < p < (N + 2)/(N - 2), N >= 3 and the potential V is radially symmetric. We construct positive clustering solutions in an annulus having O(1/epsilon) critical points, as well as sign changing solutions with O(1/epsilon) zeroes concentrating near zero.