Multiple condensations for a nonlinear elliptic equation with sub-criticalgrowth and critical behaviour

We consider the following nonlinear elliptic equations {Deltau + u+N/(N-2) = 0 in Omega, {u + mu on partial derivative Omega (mu i s an unknown constant), {integral partial derivative Omega(-partial derivat iveu/partial derivativen) = M, where u(+) = max(u, 0), M is a prescribed constant, and Omega is a bounded and smooth domain in R-N, N greater than or equal to 3. It is known that fo r M = M*((N)), Omega = B-R(0), the above problem has a continuum of solutio ns. The case when M > M*((N)) is referred to as supercritical in the litera ture. We show that for M near KM*((N)), K > 1, there exist solutions with m ultiple condensations in Omega. These concentration points axe non-degenera te critical points of a function related to the Green's function.