Multiple Sign Changing Solutions of Nonlinear Elliptic Problems in Exterior Domains

We consider the problem -Delta u + (V-infinity + V(x))u = vertical bar u vertical bar(p-2) u, u is an element of H-0(1)(Omega), where Omega is an exterior domain in R-N, V-infinity > 0, V is an element of C-0 (R-N), inf(R)(N) V > -V-infinity and V(x) -> 0 as vertical bar x vertical bar -> infinity. Under symmetry conditions on Omega and V. and some assumptions on the decay of V at infinity, we show that there is an effect of the topology of the orbit space of certain subsets of the domain on the number of low energy sign changing solutions to this problem.