Vol. 278, No. 2, 2015

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

Yi Fang and María del Mar González

Vol. 278 (2015), No. 2, 369–405

In this paper, we analyze the asymptotic behavior of Palais–Smale sequences associated to 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 solution for the fractional Yamabe equation on Euclidean space. We also verify the noninterfering fact for multibubbles.

fractional Yamabe problem, Palais–Smale sequences
Mathematical Subject Classification 2010
Primary: 35J70
Secondary: 58J32
Received: 20 October 2014
Accepted: 23 March 2015
Published: 6 October 2015
Yi Fang
School of Mathematical Sciences
University of Science and Technology of China
GuanLi-KeYan Building
96 Jinzhai Road, Hefei
230026 Anhui
María del Mar González
ETSEIB – Departament de Matematica Aplicada I
Universitat Politecnica de Catalunya
Avenida Diagonal, 647
08028 Barcelona