Existence of infinitely many solutions for singular semilinear problems on exterior domains

Abstract

In this article we prove the existence of infinitely many radial solutions of ∆u + K(r)ƒ(u) = 0 on the exterior of the ball of radius R > 0, B_R, centered at the origin in ℝ^N with u = 0 on ∂B_R and lim_r→∞ u(r) = 0 where N > 2, ƒ is odd with ƒ < 0 on (0, β), ƒ < 0 on (β, ∞), ƒ is superlinear for large u, ƒ(u) ~ -1/(|u|^q-1u) with 0 < q < 1 for small u, and 0 < K(r) ≤ K₁/r^α with N + q(N - 2) < α < 2(N - 1) for large r.