Arbitrary many boundary peak solutions for an elliptic Neumann problem with critical growth

We consider the following problem, -Delta u + mu u = u(2*-1), u > 0 in Omega, partial derivative u/partial derivative n = 0 on partial derivative Omega, where mu > 0 is a large parameter, Omega is a bounded domain in R-N, N >= 3 and 2* = 2N/(N - 2). Let H(P) be the mean curvature function of the boundary. Assuming that H(P) has a local minimum point with positive minimum, then for any integer k, the above problem has a k-boundary peaks solution. As a consequence, we show that if Omega is strictly convex, then the above problem has arbitrarily many solutions, provided that mu is large. (C) 2007 Elsevier Masson SAS. All rights reserved.