Existence of solutions for semilinear problems on exterior domains

In this article we prove the existence of an infinite number of radial solutions to \(Δ u+K(r)f(u)=0\) on \(RN\) such that \(limr → ∞ u(r)=0\) with prescribed number of zeros on the exterior of the ball of radius R>0 where f is odd with f<0 on \((0,β)\), f>0 on \((β,∞)\) with f superlinear for large \(u\), and \(K(r) ~ r-α\) with \( α > 2(N-1)\). For more information see https://ejde.math.txstate.edu/Volumes/2020/34/abstr.html