  In this paper we study the problem of prescribing the Gaussian curvature
under a conformal change of the metric. We are concerned with the problem posed
on a subdomain of the 2-sphere under Neumann boundary conditions of the
conformal factor.
  If the area of the subdomain is greater than 2\pi, the associated energy
functional is no longer bounded from below. We treat this case by using min-max
techniques, giving a new existence result that generalizes and unifies previous
work on the argument.
