Abstract

This article is devoted to the study of radially symmetric solutions to the nonlinear Schrödinger equation 2 Δ u - V(r)u + |u| {p-1}u = 0, in B, { u}{ n} = 0, { on},{}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/) critical points, as well as sign changing solutions with O(1/) zeroes concentrating near zero. © 2007 Springer-Verlag.