Existence of solutions for semilinear problems on exterior domains

Abstract

In this article we prove the existence of an infinite number of radial solutions to \(\Delta u+K(r)f(u)=0\) on \(\mathbb{R}^{N}\) such that \(\lim_{r \to \infty} u(r)=0\) with prescribed number of zeros on the exterior of the ball of radius R>0 where f is odd with f<0 on \((0,\beta)\), f>0 on \((\beta,\infty)\) with f superlinear for large \(u\), and \(K(r) \sim r^{-\alpha}\) with \( \alpha > 2(N-1)\). For more information see https://ejde.math.txstate.edu/Volumes/2020/34/abstr.html