Electronic Journal of Differential Equations, Vol. 2024 (2024), No. 06, pp. 1-14.

Title: Existence of two infinite families of solutions for singular superlinear equations on exterior domains
       
Author: Joseph Iaia (Univ. of North Texas, Denton, TX, USA)

Abstract: 
In this article we study radial solutions of $\Delta u + K(|x|) f(u) =0$ in
the exterior of the ball of radius $R>0$ in $\mathbb {R}^{N}$ with $N>2$ where
$f$ grows superlinearly at infinity and is singular at $0$ with
$f(u) \sim \frac{1}{|u|^{q-1}u}$ and $0<q<1$ for small $u$.
We assume $K(|x|) \sim |x|^{-\alpha}$ for large $|x|$ and establish existence of
two infinite families of  sign-changing solutions when  $N+q(N-2) <\alpha <2(N-1)$.

Submitted July 13, 2023. Published January 23, 2024.
Math Subject Classifications: 34B40, 35B05.
Key Words: Exterior domains; singular; semilinear; radial solution.