Multiple Sign Changing Solutions of Nonlinear Elliptic Problems in Exterior Domains

Abstract

Abstract We consider the problem −Δu + (V∞ + V(x))u = |u|p−2 u, u ∈ H0 1 (Ω), where Ω is an exterior domain in ℝN, V∞ > 0, V ∈ C0(ℝN), infℝN V > −V∞ and V(x) → 0 as |x| → ∞. Under symmetry conditions on Ω 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.