Article proving the existence of infinitely many radial solutions of ∆𝓊+𝐾(𝓇) ƒ (𝓊) = 0 on the exterior of the ball of radius R > 0, BR, centered at the origin in ℝᴺ with u = 0 on ∂BR and lim/r→∞ 𝓊(𝓇) = 0 where N > 2, f is odd with f < 0 on (0, β), f > 0 on (β, ∞), f is superlinear for large u, ƒ(𝓊) ∼ −1/(|𝓊|𝘲⁻¹𝓊) with 0 < q < 1 for small u, and 0 < 𝐾(𝓇) ≤ 𝐾₁/r∝ with 𝑁 + q(𝑁 − 2) < ∝ < 2(𝑁− 1) for large r.