Clustered solutions to low-order perturbations of fractional Yamabe equations

Abstract

Let (X, g(+)) be an asymptotically hyperbolic manifold and (M, [(h) over cap]) be its conformal infinity. We construct positive clustered solutions to low-order perturbations of gamma-Yamabe equations (0 < gamma < 1) on (M, (h) over cap), which are slightly supercritical, under certain geometric and dimensional assumptions. These solutions certainly exhibit non-isolated blow-up.