We prove some existence and non-existence results for a nonlinear elliptic equation involving cylindrical weights and critical growth. More precisely, defining xi = (x, y) epsilon R-k x RN-k, we study the variational problem
{-div(vertical bar x vertical bar(a)del u) = lambda vertical bar x vertical bar(a-2)u + vertical bar x vertical bar(-b)u(p-1) in R-N, x not equal 0 u >= 0 under suitable assumptions for the parameters p epsilon (2, 2*) and a, lambda, b epsilon R. We firstly consider the strongly elliptic case a = 0. (C) 2007 Elsevier Ltd. All rights reserved.
