Qualitative properties of singular solutions to the fractional Yamabe problem Cruz-Blázquez, Sergio Dela Torre, Azahara Ruiz Aguilar, David Isolated singularities Fractional Yamabe problem Nonlocal ODE Morse index S.C. is supported by the project Quantitative and qualitative aspects of nonlinear PDEs from the University of Campania Luigi Vanvitelli, funded under the MIUR bando 2017 PRIN - JPCAP. Part of this work was carried out during his visit to the University “Sapienza Universit`a di Roma”, to which he is grateful. A. DlT acknowledges financial support from the Spanish Ministry of Science and Innovation (MICINN) through the grant Juan de la Cierva-Incorporaci´on 2018 with ref. IJC2018-036320-I and from the Spanish Government through the grant MTM2017-85757-P (MICIU). She is also supported by Fondi Ateneo – Sapienza Universit`a di Roma. The three autors have been supported by the FEDER-MINECO Grant PID2021-122122NB-I00 and by J. Andalucia (FQM-116). A. DlT and D. R. also acknowledge financial support from the Spanish Ministry of Science and Innovation (MICINN), through the IMAG-Maria de Maeztu Excellence Grant CEX2020-001105- M/AEI/10.13039/501100011033. In this paper we are interested in the qualitative properties of the solutions to the fractional Yamabe problem in Rn which present an isolated singularity. In particular, we prove that the Morse index of any such solution is infinity. The proof uses an Emden Fowler type transformation, so that we can pass to a nonlocal 1D problem posed in R. 2023-11-22T11:56:16Z 2023-11-22T11:56:16Z 2023-04-12 journal article Published version: Sergio Cruz-Blázquez, Azahara DelaTorre, David Ruiz. Qualitative properties of singular solutions to the fractional Yamabe problem. Discrete and Continuous Dynamical Systems, 2023, 43(11): 4027-4041. [doi: 10.3934/dcds.2023077] https://hdl.handle.net/10481/85824 10.3934/dcds.2023077 eng http://creativecommons.org/licenses/by-nc-nd/4.0/ open access Attribution-NonCommercial-NoDerivatives 4.0 Internacional Cornell University