Existence of solutions for semilinear problems on exterior domains

Abstract

In this article we prove the existence of an infinite number of radial solutions to ∆u + K(r)ƒ(u) = 0 on ℝN such that lim r→∞ u(r) = 0 with prescribed number of zeros on the exterior of the ball of radius R > 0 where ƒ is odd with ƒ < 0 on (0, β), ƒ > 0 on (β, ∞) with ƒ superlinear for large u, and K(r) ∼ r-α with α > 2 (N - 1).