Radial solutions for the Brezis–Nirenberg problem involving large nonlinearities

Let us consider the problem ⎧⎨⎩ − u +a |x| u = up in B1, u>0 in B1, u =0 on ∂B1, (0.1) where B1 is the unit ball in RN, N 3, and a(|x|) 0 is a smooth radial function. Under some suitable assumptions on the regular part of the Green function of the operator−u − N−1 r u+ a(r)u, we prove the existence of a radial solution to (0.1) for p large enough. © 2008 Elsevier Inc. All rights reserved.