Electronic Journal of Differential Equations, 
Vol. 2021 (2021), No. 03, pp. 1-17.

Title: Existence and nonexistence for singular sublinear problems on exterior domains
       
Authors: Mageed Ali  (Univ. of North Texas, Denton, TX, USA)
         Joseph A. Iaia (Univ. of North Texas, Denton, TX, USA)

Abstract:
 In this article we study the existence of radial solutions of $\Delta u + K(|x|)f(u)= 0$
 on the exterior of the ball of radius R>0 centered at the origin in $\mathbb{R}^N$ with
 u=0 on $\partial B_{R}$, and $\lim_{|x| \to \infty} u(x)=0$ where N>2,
 $f(u) \sim \frac{-1}{|u|^{q-1}u} $ for u near 0 with 0<q<1, and
 $f(u) \sim |u|^{p-1}u$ for large |u| with 0<p<1.
 Also, $K(|x|) \sim |x|^{-\alpha}$ with $ N+q(N-2) < \alpha <2(N-1)$ for large |x|.

Submitted June 11, 2020. Published January 07, 2021.
Math Subject Classifications: 34B40, 35B05.
Key Words: Exterior domains; singular problem; sublinear; radial solution.