Multiple nonradial solutions for a nonlinear elliptic problem with singular and decaying radial potential

Many existence and nonexistence results are known for nonnegative radial solutions to the equation -Δu + A u / |x|^α = f(u) in R^N with N ≥ 3, A,α > 0 and nonlinearites satisfying |f(u)| ≤ (const.) u^(p-1) for some p > 2. Existence of nonradial solutions, by contrast, is known only for N ≥ 4, α = 2, f(u) = u^(2*-1) and A > 0 large enough. Here we show that the equation has multiple nonradial solutions as A → +∞ for N ≥ 4, 2/(N-1) < α < 2N-2, α ≠ 2, and nonlinearities satisfying suitable assumptions. Our argument essentially relies on the compact embeddings between some suitable functional spaces of symmetric functions, which yields the existence of nonnegative solutions of mountain-pass type, and the separation of the corresponding mountain-pass levels from the energy levels associated to radial solutions