Electronic Journal of Differential Equations, Vol. 2021 (2021), No. 68, pp. 1-17.

Title: Infinitely many solutions for a singular semilinear problem on exterior domains
       
Authors: Mageed Ali (Univ. of Kirkuk, Iraq)
         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
 Δ U + K(x)f(U)= 0 on the exterior of the ball of radius R>0 centered at the
 origin in R<sup>N</sup> with U=0 on $\partial B_{R}$, and
 $\lim_{|x| \to \infty} U(x)=0$ where N&gt;2,
 $f(U) \sim \frac{-1}{|U|^{q-1}U} $ for small $U \neq 0$ with 0&lt;q&lt;1, and
 $f(U) \sim |U|^{p-1}U$ for large |U| with p&gt;1. Also, 
 $K(x) \sim |x|^{-\alpha}$  with &alpha;&gt;2(N-1) for large |x|.

Submitted November 2, 2020. Published August 10, 2021.
Math Subject Classifications: 34B40, 35B05.
Key Words: Exterior domain; semilinear equation; radial solution.