Clustered solutions for supercritical elliptic equations on Riemannian manifolds

Let (M, g) be a smooth compact Riemannian manifold of dimension n >= 5. We are concerned with the following elliptic problem: -Delta(g )u + a(x)u = u(n)(+)(2/n)(-2+epsilon), u > 0 in M , where Delta(g) = div(g) (del) is the Laplace-Beltrami operator on M, a(x) is a C-2 function on M such that the operator -Delta(g) + a is coercive, and epsilon > 0 is a small real parameter. Using the Lyapunov -Schmidt reduction procedure, we obtain that the problem under consideration has a k-peaks solution for positive integer k >= 2, which blow up and concentrate at one point in M.