Abstract
In this paper we consider the following nonlinear critical problem: -Delta u = (1 +epsilon K-0(0)(x))u(n=2/n-2), u > 0 in Omega, u = 0, on partial derivative Omega, where Omega is a bounded domain of R-n, K-0 is a given function and so is a small parameter. Under the assumption that Ko is flat near its critical points, we prove an existence result in terms of the Euler-Hopf index. We believe that it is the very first result in this direction that we do not need any restrictions on the flatness coefficient.