Electronic Journal of Differential Equations,
Vol. 2019 (2019), No. 108, pp. 1-11.

Title: Existence of infinitely many solutions for
       singular semilinear problems on exterior domains

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

Abstract:
 In this article we prove the existence of infinitely many radial solutions
 of $\Delta u + K(r)f(u)= 0$ on the exterior of the ball of radius R>0,
 $B_R$, centered at the origin in $\mathbb{R}^N$ with
 u=0 on $\partial B_R$ and $\lim_{r \to \infty} u(r)=0$ where N>2,
 f is odd with f<0 on $(0, \beta) $, f>0 on $(\beta, \infty)$,
 f is superlinear for large u, $f(u) \sim-1/(|u|^{q-1}u)$ with
 0&lt;q&lt;1 for small u, and $0< K(r) \leq K_1/r^{\alpha}$
 with $N+q(N-2) < \alpha< 2(N-1) $ for large r.


Submitted March 9, 2018. Published September 23, 2019.
Math Subject Classifications: 34B40, 35B05.
Key Words: Exterior domain; semilinear; singular; superlinear; radial solution.