Electronic Journal of Differential Equations, 
Vol. 2020 (2020), No. 34, pp. 1-10.

Title: Existence of solutions for semilinear problems on exterior domains

Authors: Joseph Iaia (Univ. of North Texas, Denton, TX, USA)

Abstract:
 In this article we prove the existence of an infinite number of radial solutions
 to $\Delta u+K(r)f(u)=0$ on $\mathbb{R}^{N}$ such that $\lim_{r \to \infty} u(r)=0$
 with prescribed number of zeros on the exterior of the ball of radius R>0
 where f is odd with f<0 on $(0,\beta)$, f>0 on $(\beta,\infty)$ with
 f superlinear for large $u$, and $K(r) \sim r^{-\alpha}$ with $ \alpha > 2(N-1)$.
 
Submitted January 12, 2019. Published April 15, 2020.
Math Subject Classifications: 34B40, 35B05.
Key Words: Exterior domain; superlinear; radial solution.