Infinite multiplicity for an inhomogeneous supercritical problem in entire space

Let K(x) be a positive function in ℝ^N, N ≥ 3 and satisfy lim_|x|→∞ K(x) = K_∞ where K _∞ is a positive constant. When p > N+1/N-3, N ≥ 4, we prove the existence of infinitely many positive solutions to the following supercritical problem: Δu(x) + K(x)u^p = 0, u > 0 in ℝ^N, lim_|x|→∞ u(x) = 0. If in addition we have, for instance, lim_|x|→∞ |x|^μ(K(x)- K_∞) = C₀ ≠ 0, 0 < μ ≤ N - 2p+2/p-1, then this result still holds provided that p > N+2/N-2.