Existence and nonexistence for singular sublinear problems on exterior domains

Abstract

In this article we study the existence of radial solutions of 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 u near 0 with 0 < q < 1, and ƒ(u) ~ |u|p-1u for large |u| with 0 < p < 1. Also, K (|x|) ~ |x|-α with N + q(N - 2) < α < 2(N - 1) for large |x|.