Existence of two infinite families of solutions for singular superlinear equations on exterior domains

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 \(N+q(N-2) <\alpha <2(N-1)\).

For more information see https://ejde.math.txstate.edu/Volumes/2024/06/abstr.html