Bubbling solutions for supercritical problems on manifolds

Abstract

Let (M, g) be an n-dimensional compact Riemannian manifold without boundary and Gamma be a non-degenerate closed geodesic of (M, g). We prove that the supercritical problem

-Delta(g)u + hu = u(n+1/n+3) (+/-) (epsilon), u > 0, in (M, g)

has a solution that concentrates along Gamma as e goes to zero, provided the function h and the sectional curvatures along Gamma satisfy a suitable condition. A connection with the solution of a class of periodic Ordinary Differential Equations with singularity of attractive or repulsive type is established.