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, \ 00 in R^N 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<α2.