Existence and nonexistence of sign-changing solutions for linearly perturbed superlinear equations on exterior domains

In this paper, we study radial solutions of Δu + K(|x|) f(u)+ (N-2)² u|x|2+(N-2)δ =0, \ 0<δ<2 in the exterior of the ball of radius $R>0$ in RN where f grows superlinearly at infinity and is singular at $0$ with f(u) ~ -1|u|q-1u and $0<q<1$ for small u. We assume K(|x|) ~ |x|-α for large $|x|$ and establish the existence of an infinite number of sign-changing solutions when $N+q(N-2) <α<2(N-1).$ We also prove nonexistence for 0<α≤2.