(untitled) (Journal of Partial Differential Equations, 2020)
In this paper we prove the existence of an infinite number of radial solutions of Δ u + K(r)f(u)= 0 on the exterior of the ball of radius R>0 centered at the origin in R^N where f is odd with f0 on (β, δ), f0 for u> δ, and where the function K(r) is assumed to be positive and K(r)→ 0 as r → ∞. The primitive F(u) = _0^u f(s) ds has a ``hilltop'' at u=δ which allows one to use the shooting method to prove the existence of solutions.