Asymptotic behavior of Palais-Smale sequences associated with fractional Yamabe type equations

In this paper, we analyze the asymptotic behavior of Palais-Smale sequences associated with fractional Yamabe type equations on an asymptotically hyperbolic Riemannian manifold. We prove that Palais-Smale sequences can be decomposed into the solution of the limit equation plus a finite number of bubbles, which are the rescaling of the fundamental solutions to the fractional Yamabe equation on Euclidean space. We also verify the non-interfering fact for multi-bubbles.