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 a Emden Fowler type transformation, so that we can pass to a nonlocal 1D problem posed in ℝ.
QUALITATIVE PROPERTIES OF SINGULAR SOLUTIONS TO THE FRACTIONAL YAMABE PROBLEM / Cruz-Blázquez, S.; Delatorre, A.; Ruiz, D.. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. - ISSN 1078-0947. - 43:11(2023), pp. 4027-40441. [10.3934/dcds.2023077]
QUALITATIVE PROPERTIES OF SINGULAR SOLUTIONS TO THE FRACTIONAL YAMABE PROBLEM
DelaTorre A.
;
2023
Abstract
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 a Emden Fowler type transformation, so that we can pass to a nonlocal 1D problem posed in ℝ.File allegati a questo prodotto
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