Radial solutions for the Brezis–Nirenberg problem involving large nonlinearities

Let us consider the problemequation(0.1){−Δu+a(|x|)u=upin B1,u>0in B1,u=0on ∂B1, where B1B1 is the unit ball in RNRN, N⩾3N⩾3, and a(|x|)⩾0a(|x|)⩾0 is a smooth radial function.Under some suitable assumptions on the regular part of the Green function of the operator −u″−N−1ru+a(r)u, we prove the existence of a radial solution to (0.1) for p large enough.