Existence and nonexistence for singular sublinear problems on exterior domains

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 \(|x|\). For more information see https://ejde.math.txstate.edu/Volumes/2021/03/abstr.html