Abstract
In this paper, we study the critical fractional nonlinear PDE: \((-\Delta )^{s}u= u^\frac{n+2s}{n-2s}\), \({u>0}\) in \(\Omega \) and \(u=0\) on \(\partial \Omega \), where \(\Omega \) is a thin annuli-domain of \({\mathbb{R}}^n, n\ge 2.\) We compute the evaluation of the difference of topology induced by the critical points at infinity between the level sets of the associated variational function. Our Theorem can be seen as a nonlocal analog of the result of Ahmedou and El Mehdi (Duke Math J 94:215–229, 1998) on the classical Yamabe-type equation.
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“This article is part of the section "Theory of PDEs" edited by Eduardo Teixeira.”
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Abdullah Sharaf, K., Chtioui, H. The topological contribution of the critical points at infinity for critical fractional Yamabe-type equations. SN Partial Differ. Equ. Appl. 1, 11 (2020). https://doi.org/10.1007/s42985-020-00011-5
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DOI: https://doi.org/10.1007/s42985-020-00011-5