We deal with the quasilinear Schrodinger equation -div(vertical bar del u vertical bar p-2 del u) + (lambda a(x) + 1)vertical bar u vertical bar(p-2) u = vertical bar u vertical bar(q-2)u, u is an element of W-1,W-p(R-N), where 2 <= p < N, lambda > 0, and p < q < p* = Np/(N - p). The potential a >= 0 has a potential well and is invariant under an orthogonal involution of RN. We apply variational methods to obtain, for), large, existence of solutions which change sign exactly once. We study the concentration behavior of these solutions as lambda -> infinity. By taking q close p*, we also relate the number of solutions which change sign exactly once with the equivariant topology of the set where the potential a vanishes. (c) 2004 Elsevier Inc. All rights reserved.3041170188