Infinitely many solutions for a semilinear problem on exterior domains with nonlinear boundary condition

Abstract

In this article we prove the existence of an infinite number of radial solutions to ∆u + K(r)ƒ(u) = 0 with a nonlinear boundary condition on the exterior of the ball of radius R centered at the origin in ℝ^N such that lim_r→∞ u(r) = 0 with any given number of zeros where ƒ : ℝ → ℝ is odd and there exists a β > 0 with ƒ < 0 on (0, β), ƒ > 0 on (β, ∞) with ƒ superlinear for large u, and K(r) ~ r^-α with 0 < α < 2(N - 1).