On some nonlinear equations with critical exponents

Consider the problem − u +f |x| λ u λ2 = |u| 4 N−2 u in B1, u =0 on ∂B1, where B1 denotes the open unit ball in RN, N 3 and λ > 0. Under some general assumptions on f, we prove the existence or the non-existence of radial solutions.We consider also the case when λ is determined. © 2008 Elsevier Inc. All rights reserved