ON SPIKE SOLUTIONS FOR A SINGULARLY PERTURBED PROBLEM IN A COMPACT RIEMANNIAN MANIFOLD

] Let (M, g) be a smooth compact riemannian manifold of dimension N >= 2 with constant scalar curvature. We are concerned with the following elliptic problem -epsilon(2)Delta(g)u + u = u(p-1), u > 0, in M. where Delta(g) is the Laplace-Beltrami operator on M, p > 2 if N = 2 and 2 < p < 2N/N - 2 if N >= 3, epsilon is a small real parameter. We prove that there exist a function Xi such that if xi(0) is a stable critical point of Xi(xi) there exists epsilon(0) > 0 such that for any epsilon is an element of (0, epsilon(0)), problem (1) has a solution u(epsilon) which concentrates near xi(0) as epsilon tends to zero. This result generalizes previous works which handle the case where the scalar curvature function of (M, g) has non-degenerate critical points.