On some nonlinear equations with critical exponents

Consider the problem{−Δu+f(|x|λ)uλ2=|u|4N−2uinB1,u=0on∂B1, where B1B1 denotes the open unit ball in RNRN, N⩾3N⩾3 and λ>0λ>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.