On the Ambrosetti–Malchiodi–Ni conjecture for general submanifolds

Artículo de publicación ISIWe study positive solutions of the following semilinear equation epsilon 2 Delta((g) over bar)u - V(z)u + u(p) = o on M, where (M, (g) over bar) is a compact smooth n-dimensional Riemannian manifold without boundary or the Euclidean space R-n, epsilon is a small positive parameter, p > 1 and V is a uniformly positive smooth potential. Given k = 1,...,n - 1, and 1 0 and positive solutions u(epsilon) that concentrate along K. This result proves in particular the validity of a conjecture by Ambrosetti et al. [1], extending a recent result by Wang et al. [32], where the one co-dimensional case has been considered. Furthermore, our approach explores a connection between solutions of the nonlinear Schredinger equation and f -minimal submanifolds in manifolds with density