Infinitely many solutions for a singular semilinear problem on exterior domains

Abstract

In this article we prove the existence of an infinite number of radial solutions to \(\Delta U + K(x)f(U)= 0\) 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 small \(U \neq 0\) with \(0<q<1\), and \(f(U) \sim |U|^{p-1}U\) for large \(|U|\) with \(p>1\). Also, \(K(x) \sim |x|^{-\alpha}\) with \( \alpha >2(N-1)\) for large \(|x|\). For more information see https://ejde.math.txstate.edu/Volumes/2021/68/abstr.html