Infinitely many solutions for a singular semilinear problem on exterior domains

Abstract

In this article we prove the existence of an infinite number of radial solutions to ΔU + K(x)ƒ(U) = 0 on the exterior of the ball of radius R > 0 centered at the origin in ℝN with U = 0 on ∂BR, and lim|x|→∞ U(x) = 0 where N > 2, ƒ(U) ~ -1/|U|q-1U for small U ≠ 0 with 0 < q < 1, and ƒ(U) ~ |U|p-1U for large |U| with p > 1. Also, K(x) ~ |x|-α with α > 2(N - 1) for large |x|.